user8210: From the meditation podcasts I have heard when a thought comes up acknowledge it by saying "thinking" and then try to gently return back to your breath. 
There is something else I tried experimentally. In this case I was not noticing my breath, but was noticing my thoughts. I did this by asking, "what's the next thought" and tried to observe my thoughts mindfully. Obviously more thoughts arose, but it felt like I was still practicing mindfulness. And it seems easier to do this type of mindfulness while in an environment with a lot of distractions. (Walking, running, etc.)
I wanted to know if it is ok to do this?
Also, are there other methods for handling my thoughts?

user4742: It is important to understand what is meant by 'right view' (samma ditti) which covers the origination of thoughts, the causal arising of thoughts, and the non-self nature of thoughts and the entire thinking apparatus.  
This understanding will help one to be mindful of the arising and passing away of thoughts during meditation without identifying with them. The default view that a thought is mine, created by myself naturally causes one to pursue them. While the right view of the true nature of thoughts eventually leads one to be unbounded from thinking. 

user7548: The thing I've learned from meditation so far: Don't try to be clever, just follow the instructions!
Anapanasati (meditation on the breath) works just the way it should be. It was highly recommended by the Buddha himself and successfully used for the last ~2500 years now. It's really simple: When you breath out, know you breath out.
If you want to develop samadhi (concentration is a misleading term, let's just call it peaceful stillness), then the best way is to choose an mediation object (breath, metta, walking, ...) and follow the instructions.

In this case I was not noticing my breath but was noticing my thoughts I did it by asking "what's the next thought " and tried to observe my thoughts mindfully

Don't do this. You will eventually get caught up in thinking and emotions. In meditation (samatha) thoughts are a distraction. They pull you away from your object of meditation. So dropping your meditation object will pretty much end your meditation.
Dealing with distracting thoughts
I guess half of all questions in this SE relate to that topic, so I'm just gonna link some instructions. In general, you have to find out by trying what works and what doesn't. What makes you (your breath) more peaceful and what makes it more stressful.
https://youtu.be/oeJ2LaFaDCY?t=53
https://www.youtube.com/playlist?list=PL603BD0B03E12F5A1 (you probably heard this)

And it seems it is easier to do this type of mindfulness when in an environment with a lot of distraction . (Walking or running etc.)

I myself noticed that in such a environment it's very beneficial to 'sort' those distraction in regards to the six senses. This is seeing, hearing, thinking, tasting, feeling, smelling.

8210: <p>From the meditation podcasts I have heard when a thought comes up acknowledge it by saying "thinking" and then try to gently return back to your breath. </p>

<p>There is something else I tried experimentally. In this case I was not noticing my breath, but was noticing my thoughts. I did this by asking, "what's the next thought" and tried to observe my thoughts mindfully. Obviously more thoughts arose, but it felt like I was still practicing mindfulness. And it seems easier to do this type of mindfulness while in an environment with a lot of distractions. (Walking, running, etc.)</p>

<p>I wanted to know if it is ok to do this?</p>

<p>Also, are there other methods for handling my thoughts?</p>
 4742: <p>It is important to understand what is meant by 'right view' (samma ditti) which covers the origination of thoughts, the causal arising of thoughts, and the non-self nature of thoughts and the entire thinking apparatus.  </p>

<p>This understanding will help one to be mindful of the arising and passing away of thoughts during meditation without identifying with them. The default view that a thought is mine, created by myself naturally causes one to pursue them. While the right view of the true nature of thoughts eventually leads one to be unbounded from thinking. </p>
 7548: <p>The thing I've learned from meditation so far: Don't try to be clever, just follow the instructions!</p>

<p>Anapanasati (meditation on the breath) works just the way it should be. It was highly recommended by the Buddha himself and successfully used for the last ~2500 years now. It's really simple: When you breath out, know you breath out.</p>

<p>If you want to develop <strong>samadhi</strong> (<em>concentration</em> is a misleading term, let's just call it <em>peaceful stillness</em>), then the best way is to choose an mediation object (breath, metta, walking, ...) and follow the instructions.</p>

<blockquote>
  <p>In this case I was not noticing my breath but was noticing my thoughts I did it by asking "what's the next thought " and tried to observe my thoughts mindfully</p>
</blockquote>

<p>Don't do this. You will eventually get caught up in thinking and emotions. In meditation (<em>samatha</em>) thoughts are a distraction. They pull you away from your object of meditation. So dropping your meditation object will pretty much end your meditation.</p>

<p><strong>Dealing with distracting thoughts</strong></p>

<p>I guess half of all questions in this SE relate to that topic, so I'm just gonna link some instructions. In general, you have to find out by trying what works and what doesn't. What makes you (your breath) more peaceful and what makes it more stressful.</p>

<p><a href="https://youtu.be/oeJ2LaFaDCY?t=53" rel="nofollow">https://youtu.be/oeJ2LaFaDCY?t=53</a></p>

<p><a href="https://www.youtube.com/playlist?list=PL603BD0B03E12F5A1" rel="nofollow">https://www.youtube.com/playlist?list=PL603BD0B03E12F5A1</a> (you probably heard this)</p>

<blockquote>
  <p>And it seems it is easier to do this type of mindfulness when in an environment with a lot of distraction . (Walking or running etc.)</p>
</blockquote>

<p>I myself noticed that in such a environment it's very beneficial to 'sort' those distraction in regards to the six senses. This is seeing, hearing, thinking, tasting, feeling, smelling.</p>
