You have to be careful and stay away from the tourist traps but was reading this morning about Uthai's Gems in the Sukhumvit area. Try a google search can't remember where I found the link. Whatever you do don't go to anywhere a taxi driver suggests as they are on a commission and stay away from the Gems Gallery, extremely overpriced. Good Luck.

Go to any gold shop, they will sell white gold also, the shop displays the current price of gold in the window, about 14400baht per Baht=(15.16grams) and shops look similar to the one below, mostly Thai Chinese owned. Bought my Wifes white gold wedding ring in Central store Bang Na.

As mk61 says steer clear of a taxi taking you to a gold shop, there are plenty of gold shops around, you will see them at MBK store, Emporium, and any of the big stores. (a shop within the store)

http://www.thaigoldjewelry.com/

Talking to my wife she tells me ring cost 4000baht including inscription
inside the ring with both of our christian names and date 2001, gold price has gone mad since then.

Both my daughter and I have both bought diamond ring's from Patty Gem's. It is inside a big department store just outside Childlom Station.We have both had them valued back home and they are worth alot more than we both paid.