You can do many things in Thailand - time permitting! If your time is short skip Phuket because it is way on the bottom of Thailand and the most expensive place to visit.
Start with a few days in Bangkok! Most flights are booked to Bangkok anyway. During this time you can book flights or train rides to the northern Thailand city of Chiang Mai. (In Chiang Mai and Bangkok you can get tours through local travel agencies if you want on short notice.) In Chiang Mai you can visit Long Neck Women Villages, Chiang Rai/Golden Triangle and other local attractions such as visiting elephants and shopping. Many tourists feel that you will see more of the "real" Thailand up north.
Spend a final night or two in Bangkok before you go home. You can take in a few tours, maybe a dinner cruise and do some last minute shopping. You will also be close enough to the airport so you can take a meter taxi to get there when you fly home.
For Bangkok get a hotel on or near the Skytrain route. This way you can use this efficient rail service to get around the city. For Chiang Mai the over night sleeper train is popular but you can also use buses or fly. There are other beaches other than Phuket that are closer to Bangkok.
http://www.urbanrail.net/as/bang/bangkok.htm
Read up on Thailand, visit a library and check out some travel guides. This way you will be able to see what you like and then plan your trip around that. You can also use the below travel forums for specific questions too.
http://www.tripadvisor.com/ShowForum-g293915-i3686-Thailand.html
http://forum.virtualtourist.com/forum-1943-1-Travel-Thailand-1-forum.html
http://www.lonelyplanet.com/thorntree/forum.jspa?forumID=51
A Lonely Planet Travel Guide is helpful if you are on a tight budget. Frommers and Fodor's Travel Guides are often used by tourists with more spending money. But plan a budget first and see what you can afford and ask for hotel recommendation in your price range. A quick Google check will give you the "things to see and do" in various cities.
http://www.asiatraveltips.com/ThingstodoinBangkok.shtml
http://www.virtualtourist.com/travel/Asia/Thailand/Northern_Thailand/Chiang_Mai-1445733/Things_To_Do-Chiang_Mai-TG-C-1.html
Good luck.