Chaing mai is a bit sleepy for me, Phuket was awsome when i went last year, lots of pubs/clubs and they dont care if your underage, just watch them lady boys.
Chaing mai = elephants, monkeys, in the mountains.
Phuket = Bars/clubs beach/ dirty old fat russians on the beach.
Bangkok = SHIT HOLE, the most depressing place on earth, and it has the fat russians aswell. you cant go into a shoping complex without being checked for explosives. oh and you have black snot at the end of each day
hope this helps, imo spend the least ammount of time in bangkok and the most time in Phuket. and try and go to Phi Phi island if you can afford it, its a 2 hour trip by sea to where they filmed "the beach" . peace.