you've got to decide if you want city or beach. also, i wouldn't rule out chiang mai...it's more laid back than bangkok and cooler than phuket IMO. you really should just move to where you're interested in, then decide from there what you like best...or travel to each for a bit and make up your mind.
phuket is where australian tourists go to get drunk and lay on the beach...it's very scenic...but it's also extremely touristy. bangkok is one of the most visited places on earth, but it's also HUGE. the internet is fine in bangkok and phuket and it won't be hard at all to get internet. bangkok is far more advanced than most places in the US in a lot of ways and most ISPs are used to foreigners wanting internet/phones/TV (so it's an extremely easy process).
i would be a bit worried about the quality of food in phuket. it's not going to be anywhere near as good as what you can get in bangkok/chiang mai if you know thai people who know where all the delicious stuff is. that said, it should be pretty tasty in phuket. just more foreign food and standard thai food in phuket. bangkok has 50,000 restaurants. in my opinion, bangkok is pretty optimal because there are plenty of beaches nearby (though not nearly as nice as phuket) where you can go on the weekend and relax. plane tickets are cheap to everywhere else in asia, so it's a good base of operations IMO.
vietnam/china, as Dr. Ngo says, is very cool too. vietnam is like thailand in that the culture is very unique and the food is ridiculously good. china is obviously like that too, but huge and with lots of cultures. i lived in malaysia for five years when i was little and loved it, but i don't think that'd be where i'd go now.