Q:

Difference between "muy" and "tan"?

What's the difference between muy and tan? In what context are they used?

La ciudad de Naga no esta tan lejos desde aqui.
Mi hija es tan/muy(?) bonita.

A:

As Flamma explained they are not quite the same thing. Tan will usually involve some sort of comparison between, your daughter in this case, and something else, be it another person or thing, and actually even a hypothetic idea of beauty, if you said:
Mi hija es tan bonita.

You would be saying that My daughter is so pretty. If it was a negative:
Mi hija no es tan bonita.

It would mean My daughter is not that pretty if you compared her against the idea of beauty itself, and My daughter is not as pretty if you compared her to another tangible being.
When it comes to muy it will always mean very, like this:
Mi hija es muy/no es muy bonita.

It would just mean My daugther is very/is not very pretty.
Having said that, I'm sure your daughter would be pretty, if you were to have one.

A:

"Muy" is superlative, like "very". "Tan" is comparative, like "as".
Mi hija no es muy bonita => My daughter is not very pretty.  // It's an absolute valuation of her beauty.
Mi hija no es tan bonita => My daughter is not as pretty. // It's a comparison, a relative valuation: She is not as pretty as you said, or she is not as pretty as your daughter.

