why does the sun happen to be so close to the earth and other stars not?

Answer

In fact, you should not say that the sun happens to be close to the earth, but that the earth is close to the sun. And it’s not a coincidence either.
It all has to do with the way stars and planets form. Simply put, a star, with its planets and all kinds of smaller objects, arises from a cloud of interstellar matter that contracts, and breaks further into smaller pieces during that contraction. This is called “fragmentation”. From those small pieces, stars are eventually born. A small part of the matter from which a star forms remains around that star, and from that planets form.

The earth is therefore close to the sun because, like the other planets of the solar system, it arose together with that sun.

You will find it nicely described at:

http://www.kennislink.nl/publicaties/ontstaan-van- Sterren-en-planetensystemen