Ive spent a month in Thailand in July 2008 and it was an amazing journey. Since your only going for about 2 weeks I would recommend sticking to the north. There are no Islands there, but there are amazing jungles and scenery. Some of the must see are Chiang Mai, Chiang Rai and Pai, the last one being especially beautiful. Kanchanabury is a bit north of BK and definitely worth a visit. The bridge on the river Kwai is there, and if you’ve seen the movie it's an extra experience. There is a trek there called "the 9 waterfalls" which I highly advise. I would recommend flying from BK to Chiang Mai, which is cheap and quick. I took the bus there and even though it's an experience, being short on time is something to consider. I did not venture to the far North-East on the country, but there are many amazing sights there as well. Try booking a jeep tour through the north; having a guide with you that knows where to go and where to take you is a huge benefit; the north is too vast for self exploration (believe me I tried). Visit the Tiger and Monkey temples, the Chiang Mai wat (temple), the floating night markets and the golden triangle.
I only spent a few days in Bangkok upon arrival and prior to departure; it’s a dirty and loud city, but it does have its appeal. As far as touristy places there, I can only speak for the royal palace and the night markets. For shopping, most definitely go to the MBK, which is a huge mall. The markets have nice stuff at times but nothing to brag about. Also, bargain with EVERYONE. They expect you too! The initial prices, especially in the markets are probably 400% over what you would really pay. The Thais are very friendly; but keep in mind that they would also have a smile on while scheming you. Don’t be too worried about theft and physical harm, but take all the necessary precautions. I hid my passports and cards in my backpack, and only carried what I though I would need for the day; everything is dirt cheap. One warning though, there are many schemers there that will try to sell you "valuable gems" and other BS, assuring you that you will sell them for profit aboard; stay away. Don’t be afraid to ask for help, but try to rely mostly on yourself and have prior knowledge of what you want and where you want to go; accept help and guidance as a second source of info.
I red the Lonely Planet Thailand guide and it was very helpful, consider getting one. There are always other tourists there with you; make friends and travel together, it is both fun and safe. You will meet some crazy characters there, embrace them and you will have a great experience.
Oh, and I don't know if your going alone, with buddies or with a special someone, but regardless stay away from the Thai ladies, a lot of times they are… not.
Enjoy, and PM me if you need any other more specific info, I am abroad now but will be home in a few days, I can look up my notes and send you some links if your interested.