I know this is obvious, but Wat Phra Kaew (Grand Palace) is a great place to shoot. Yes, there are lot's of tourists there, but if you go during the week it's not so bad. If you go, please dress polite. Last time I went men were required to wear long pants, shirts with sleeves, and women were given a skirt if what they wore was too short.
Another obvious place is Ayutthaya, more specifically Wat Chaiwatthanaram. It's the ancient capitol of Siam and full of ancient statues, buildings, and chedi's.
I know the first two are where everyone goes, but I think if you come to Thailand you owe it to yourself to get some great shots from those two places as they are quite breathtaking. Kind of like going to Disneyworld and getting a shot of the castle.

One of my favorite places to shoot is Phuttamonthon (or Buddhamonthon). It is a large park with a large Buddha statue in the middle. There's not much to shoot other than the statue, but it is one of my favorites with the right lighting or cloud cover.
The Erawan Elephant Museum has a really cool room decorated in shells and if I remember right, a long dragon staircase. The upper room is a Buddhist temple. Head over to the gallery page (click link at top) to see some photos.
Thailand is one of the places you can just wander around and get great photo opportunities. We got lost once in the country and I got some nice shots of water buffalo wandering in front of the car.