I've been in Thailand for about a year and a half now, here's where I'd go:
Bangkok. I'd recommend staying in a hostel/hotel away from Khao San road, staying on Sukhumvit road would be better. Khao San road is crap, but if you do go then it's only worth it for the bars, be careful for scams and pickpockets around that area. In Bangkok you should go to visit Chatuchak market if you're there at the weekend, Siam Paragon for shopping and cinema, Soi Cowboy if you're into that, MBK for cheap fake clothes, and wherever else for touristy stuff.
If you go north, go to Chiang Mai, Pai and optionally Chiang Rai. In Chiang Mai you can do trekking, cooking and all kinds of touristy things. It's a fun place, I spent a year there. I'd recommend going to Tiger Kingdom and do some trekking with elephant riding. Pai is a really relaxed small town, you should rent scooters and go to the canyon, hot springs and watersfalls. There's a nice hostel called Spicy Pai which I stay at when I go there, it's a little bit out of town but walkable. If you have time to go to Chiang Rai, you should go to the white temple called Wat Rong Khun.
I haven't spent much time in the south, but I've been to Koh Tao and Koh Phangan. You should go for the full moon party, then head to Koh Tao for some diving. You can get a Padi diving license for a couple of hundred pounds with 5 or so days of diving and accommodation included. The company I used was called Bans Diving Resort I think. You can also do a snorkeling trip which takes you around the island to see the different places, I think I paid about a fiver for it. Avoid any jet skis, you'll definitely get scammed.
Other than that, my friend says that Krabi is good, but I haven't been there yet.