user399: After attaining Nirvana, what happens to the person(conscious) after death? 
Does the person cease to exist?
If not, does the person go to some peaceful place?

user-1: I'll take a stab at this one. The thing that needs to be understood for this is the idea of 'anatta'. This is not 'no-self' it is 'not-self'. The difference is this: 'No Self' is an opinion. A point of view. To know that there was 'no self' one would need to know everything at all times past, future and present. Holding points of view is thoroughly condemned by the Buddha as being merely opinion based on contact through the senses.
http://obo.genaud.net/dhamma-vinaya/bd/dn/dn.01.6.olds.bd_end.htm
The idea of 'not-self' is a thing which can be seen for one's self: "This" (and "That") are not self. The understanding that a thing is not self is based on the idea that if it were the self it could be controlled, such as, for example, to say that it was not to die. That cannot be, so that which is out of our control cannot be the self.
The dialog goes like this (from Vinaya Pitaka, MV 1):
"Consciousness is not self ... Inasmuch, monks, as consciousness is not self, therefore consciousness tends to sickness, and one does not get the chance to say in regard to consciousness, 'Let consciousness become such for me, let consciousness not become thus for me.'
What do you think about this, monks? Is body permanent or impermanent?"
"Impermanent, Lord."
"But is that which is impermanent painful or pleasurable?"
"Painful, Lord."
"But is it fit to consider that which is impermanent, painful, of a nature to change, as 'This is mine, this am I, this is my self'?"
"It is not Lord." ...
That understood it is to be extended to everything that has come into existence, understanding that 'that which has come into existence is subject to time, and subject to time, has a beginning, middle, and end. One of many ways Gotama used to describe 'everything in existence' was the khandhas (the stockpiles): body, sense-experience, perception, own-making and consciousness. Another was 'The All': the eye and sight, the ear and sound, the nose and scents, the tongue and tastes, the body and touch, and the mind and things.
What happens after death on attaining Nibbana (or Pari-nibbana) is best understood by first understanding how coming into existence occurs. That is the Paticca Samuppada, which is briefly: This being, that becomes, upon the ending of this, the ending of that.
Because the previously existing individual at death does not see the outcome in further pain and death in the assumption of existence, he acts in such a way as to create new existence. His identification with acts of body, speech and mind intended to create existence result in identified-with consequences taking the form of: contact with identified-with consciousness of named-shapes. "I see shapes."
If that individual had not acted in such a way as to create contact with identified-with consciousness of named-shapes, there would be no coming into identified-with existence and no coming to an end of that existence.
That is Nibbana. The sitting before, as it were, the possibility of existence and not doing that.
So it is not that 'a person' attains Nibbana, it is that 'the person,' that which has been previously identified with as 'Me' or 'my' or 'I', the khandhas, the all, is abandoned for the attaining of Nibbana.
Whatever it is that is left cannot be described because language (especially English with it's subject, verb, and object) is bound up in the terminology of existence. Nevertheless speaking conventionally there is mention of the Arahant experiencing un-identified with sense-experience (in his case the experience of sensations that are neither pleasant nor unpleasant), and consciousness (vinnana, the so-called vinnana anidassana, the unseen consciousness).
For a collection of materials on vinnana anidassana see:
http://obo.genaud.net/backmatter/glossology/green_tea/green_tea_toc.htm

user5000: 
After attaining Nirvana, what happens to the person(conscious) after death?

After attaining Nirvana, the person is and is not after death.

Does the person cease to exist?

The person does not cease to exist, nor the person exists.

If not, does the person go to some peaceful place?

The person does not go to some peaceful place, nor the person does go to some peaceful place.

user-1: This question is a useful one because: 1. it is inevitable, 2. it illustrates the kind of thing that is considered 'vexing' or leads to "thicket of views", etc. So, plunge in! Knowing what not to waste one's time on is very beneficial! 
If the Buddha refused to answer, then as everyone has said, that should tell you something. A lot of breath is wasted on debate about what exists or does not. My Self Inquiry teachers talked about there being only Two Real Things: The Void and Experience. Perhaps these correspond to Nirvana and reality as we perceive it. They are one, but that is not usually seen. 
The analogy of the flame going out - where did it go? - is a common one. I prefer this analogy: A life is like a musical performance: when it ends, it is done. It did not come from somewhere, and did not go anywhere. If it was an improvisation, like live Jazz or something, then it is not even written down. If it was not recorded, then other than peoples' memories, it has no enduring effect at all.
The key to considering such an imponderable as Death is to ask oneself: Why does this matter to me? Keep asking until you figure it out, then move on. That is Self Inquiry, which leads to Nonduality.

user120: As I understand it, Crab Bucket is correct that this is a question to which an answer is never given. I will contribute some source and try to flesh out this answer a bit:

According to the Avyakata Sutta, the Buddha says that holding a viewpoint about what happens to an enlightened one after death is 'anguish' [Pāli: 'vippatisara'] and that well-instructed, noble disciples don't declare an answer to it.
According to the Culamalunkya Sutta, the Buddha does not declare any of the ten 'speculative views' about the cosmos, the soul/body, or parinibbāna:


"Why have I left that undeclared? Because it is unbeneficial, it does
  not belong to the fundamentals of the holy life, it does not lead to
  disenchantment, to dispassion, to cessation, to peace, to direct
  knowledge, to enlightenment, to Nibbāna. That is why I have left it
  undeclared."


According to the Aggi-Vacchagotta Sutta, the Buddha says that he doesn't declare an answer to the question and that the four positions (does exist, doesn't exist, both does and doesn't exist, neither exists nor doesn't) are a 'thicket of views'. 
He then uses an analogy to illustrate why these positions don't apply to him, namely, to try to describe him after death would be like trying to pin down a fire that has gone out--where did it go? Where is it now? He then uses another simile, describing himself as 'deep, boundless, hard to fathom, like the sea.' The second simile may be intended to prevent the development of an annihilation view. (cf. Bodhi, 320, 2005)
Bodhi, B. In the Buddha’s Words: An Anthology of Discourses from the Pāli Canon, 2005.


user111: There was no person existing in the 1st place to cease to exist. What you mistake as a person is just the 5 aggregates of clinging. They are just natural processes of causes and effects. Once you attain Nibbana, the causes for continuation of the 5 aggregates are removed. Hence no continuation.

user157: In one sense he continues just as we do. Once he attained nirvana under the Bodhi tree, the Buddha carried on teaching for another 50 years. It was only on the death of his physical body that he underwent parinirvana, that is to say final release. However this just pushes the question on from nirvana to parinirvana.
The question of what happens to an enlightened being after death is one of the unanswered questions i.e. does the Tathagata (Buddha) exist after death. The Buddha refused to address metaphysical issues such as these. He teaches one thing and that thing is liberation. He views other issues such as this, the nature of the universe, the nature of the 'soul' as a distraction.
It's not to say that this isn't a good question but it is one that is deliberately unanswered by the Buddha. As such I'm probably not going to be able to do it either.
It's the answer of no answer
NOTE
This answer is based on Theravada teachings and is not the stance of all Buddhist schools. Other answers here will be from different perspectives and should be considered along with this answer.

399: <p>After attaining Nirvana, what happens to the person(conscious) after death? </p>

<p>Does the person cease to exist?</p>

<p>If not, does the person go to some peaceful place?</p>
 -1: <p>I'll take a stab at this one. The thing that needs to be understood for this is the idea of 'anatta'. This is not 'no-self' it is 'not-self'. The difference is this: 'No Self' is an opinion. A point of view. To know that there was 'no self' one would need to know everything at all times past, future and present. Holding points of view is thoroughly condemned by the Buddha as being merely opinion based on contact through the senses.
<a href="http://obo.genaud.net/dhamma-vinaya/bd/dn/dn.01.6.olds.bd_end.htm" rel="nofollow">http://obo.genaud.net/dhamma-vinaya/bd/dn/dn.01.6.olds.bd_end.htm</a>
The idea of 'not-self' is a thing which can be seen for one's self: "This" (and "That") are not self. The understanding that a thing is not self is based on the idea that if it were the self it could be controlled, such as, for example, to say that it was not to die. That cannot be, so that which is out of our control cannot be the self.</p>

<p>The dialog goes like this (from Vinaya Pitaka, MV 1):</p>

<p>"Consciousness is not self ... Inasmuch, monks, as consciousness is not self, therefore consciousness tends to sickness, and one does not get the chance to say in regard to consciousness, 'Let consciousness become such for me, let consciousness not become thus for me.'
What do you think about this, monks? Is body permanent or impermanent?"
"Impermanent, Lord."
"But is that which is impermanent painful or pleasurable?"
"Painful, Lord."
"But is it fit to consider that which is impermanent, painful, of a nature to change, as 'This is mine, this am I, this is my self'?"
"It is not Lord." ...</p>

<p>That understood it is to be extended to everything that has come into existence, understanding that 'that which has come into existence is subject to time, and subject to time, has a beginning, middle, and end. One of many ways Gotama used to describe 'everything in existence' was the khandhas (the stockpiles): body, sense-experience, perception, own-making and consciousness. Another was 'The All': the eye and sight, the ear and sound, the nose and scents, the tongue and tastes, the body and touch, and the mind and things.</p>

<p>What happens after death on attaining Nibbana (or Pari-nibbana) is best understood by first understanding how coming into existence occurs. That is the Paticca Samuppada, which is briefly: This being, that becomes, upon the ending of this, the ending of that.</p>

<p>Because the previously existing individual at death does not see the outcome in further pain and death in the assumption of existence, he acts in such a way as to create new existence. His identification with acts of body, speech and mind intended to create existence result in identified-with consequences taking the form of: contact with identified-with consciousness of named-shapes. "I see shapes."</p>

<p>If that individual had not acted in such a way as to create contact with identified-with consciousness of named-shapes, there would be no coming into identified-with existence and no coming to an end of that existence.</p>

<p>That is Nibbana. The sitting before, as it were, the possibility of existence and not doing that.</p>

<p>So it is not that 'a person' attains Nibbana, it is that 'the person,' that which has been previously identified with as 'Me' or 'my' or 'I', the khandhas, the all, is abandoned for the attaining of Nibbana.</p>

<p>Whatever it is that is left cannot be described because language (especially English with it's subject, verb, and object) is bound up in the terminology of existence. Nevertheless speaking conventionally there is mention of the Arahant experiencing un-identified with sense-experience (in his case the experience of sensations that are neither pleasant nor unpleasant), and consciousness (vinnana, the so-called vinnana anidassana, the unseen consciousness).</p>

<p>For a collection of materials on vinnana anidassana see:
<a href="http://obo.genaud.net/backmatter/glossology/green_tea/green_tea_toc.htm" rel="nofollow">http://obo.genaud.net/backmatter/glossology/green_tea/green_tea_toc.htm</a></p>
 5000: <blockquote>
  <p>After attaining Nirvana, what happens to the person(conscious) after death?</p>
</blockquote>

<p>After attaining Nirvana, the person is and is not after death.</p>

<blockquote>
  <p>Does the person cease to exist?</p>
</blockquote>

<p>The person does not cease to exist, nor the person exists.</p>

<blockquote>
  <p>If not, does the person go to some peaceful place?</p>
</blockquote>

<p>The person does not go to some peaceful place, nor the person does go to some peaceful place.</p>
 -1: <p>This question is a useful one because: 1. it is inevitable, 2. it illustrates the kind of thing that is considered 'vexing' or leads to "thicket of views", etc. So, plunge in! Knowing what not to waste one's time on is very beneficial! </p>

<p>If the Buddha refused to answer, then as everyone has said, that should tell you something. A lot of breath is wasted on debate about what exists or does not. My Self Inquiry teachers talked about there being only <strong>Two Real Things: <em>The Void</em> and <em>Experience</em></strong>. Perhaps these correspond to Nirvana and reality as we perceive it. They are one, but that is not usually seen. </p>

<p>The analogy of the flame going out - where did it go? - is a common one. I prefer this analogy: A life is like a musical performance: when it ends, it is done. It did not come from somewhere, and did not go anywhere. If it was an improvisation, like live Jazz or something, then it is not even written down. If it was not recorded, then other than peoples' memories, it has no enduring effect at all.</p>

<p>The key to considering such an imponderable as Death is to ask oneself: <strong>Why does this matter to me?</strong> Keep asking until you figure it out, then move on. That is Self Inquiry, which leads to Nonduality.</p>
 120: <p>As I understand it, Crab Bucket is correct that this is a question to which an answer is never given. I will contribute some source and try to flesh out this answer a bit:</p>

<ul>
<li>According to the <a href="http://www.accesstoinsight.org/tipitaka/an/an07/an07.051.than.html">Avyakata Sutta</a>, the Buddha says that holding a viewpoint about what happens to an enlightened one after death is 'anguish' [Pāli: 'vippatisara'] and that well-instructed, noble disciples don't declare an answer to it.</li>
<li>According to the <a href="http://www.wisdompubs.org/book/middle-length-discourses-buddha/selections/middle-length-discourses-63-culamalunkya-sutta">Culamalunkya Sutta</a>, the Buddha does not declare any of the ten 'speculative views' about the cosmos, the soul/body, or parinibbāna:</li>
</ul>

<blockquote>
  <p>"Why have I left that undeclared? Because it is unbeneficial, it does
  not belong to the fundamentals of the holy life, it does not lead to
  disenchantment, to dispassion, to cessation, to peace, to direct
  knowledge, to enlightenment, to Nibbāna. That is why I have left it
  undeclared."</p>
</blockquote>

<ul>
<li><p>According to the <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.072.than.html">Aggi-Vacchagotta Sutta</a>, the Buddha says that he doesn't declare an answer to the question and that the four positions (does exist, doesn't exist, both does and doesn't exist, neither exists nor doesn't) are a 'thicket of views'. </p>

<p>He then uses an analogy to illustrate why these positions don't apply to him, namely, to try to describe him after death would be like trying to pin down a fire that has gone out--where did it go? Where is it now? He then uses another simile, describing himself as 'deep, boundless, hard to fathom, like the sea.' The second simile may be intended to prevent the development of an annihilation view. (cf. Bodhi, 320, 2005)</p>

<p>Bodhi, B. In the Buddha’s Words: An Anthology of Discourses from the Pāli Canon, 2005.</p></li>
</ul>
 111: <p>There was no person existing in the 1st place to cease to exist. What you mistake as a person is just the <a href="http://www.beyondthenet.net/dhamma/fiveAggregates.htm">5 aggregates</a> of clinging. They are just natural processes of causes and effects. Once you attain Nibbana, the causes for continuation of the 5 aggregates are removed. Hence no continuation.</p>
 157: <p>In one sense he continues just as we do. Once he attained nirvana under the Bodhi tree, the Buddha carried on teaching for another 50 years. It was only on the death of his physical body that he underwent <a href="http://en.wikipedia.org/wiki/Parinirvana" rel="noreferrer">parinirvana</a>, that is to say final release. However this just pushes the question on from nirvana to parinirvana.</p>

<p>The question of what happens to an enlightened being after death is one of the <a href="http://en.wikipedia.org/wiki/Avyakata" rel="noreferrer">unanswered questions</a> i.e. does the Tathagata (Buddha) exist after death. The Buddha refused to address metaphysical issues such as these. He teaches one thing and that thing is liberation. He views other issues such as this, the nature of the universe, the nature of the 'soul' as a distraction.</p>

<p>It's not to say that this isn't a good question but it is one that is deliberately unanswered by the Buddha. As such I'm probably not going to be able to do it either.</p>

<p>It's the answer of no answer</p>

<p><strong>NOTE</strong></p>

<p>This answer is based on Theravada teachings and is not the stance of all Buddhist schools. Other answers here will be from different perspectives and should be considered along with this answer.</p>
