Hi and welcome to the forums! Check the "Start Here" thread at the top of the Thailand forum for a tonne of excellent recommendations for restaurants to visit in Bangkok. As for things to do in Phuket, snorkelling is a popular activity. Boat trips are good too - you can take the public ferry from Phuket to Laem Tong beach on Phi Phi, which is absolutely beautiful. Check return times first, though, so you don't get stranded. Also everything on the beach is very expensive though so bring provisions such as drinks etc with you.
You will find it is much more affordable to book tours once you arrive. Travel agents in Bangkok will be able to offer you a range of packages for Phuket too... shop around, don't just take the first one you see, as the same tour, excursion or activity is likely to be different in price at different agents.
Cheaper still is independent travel... arranging your own thing. Some people don't like the hassle and uncertainty of this but it can be fun to do your own research and then put a plan into action rather than paying somebody to do it.
Try and strike a nice balance between using your time well to see stuff and also relaxing... you don't want to be haring around in a country which it pays to be laid back and flexible in!
Last edited by steveadmin; 10th March 2012 at 10:05 AM.