I have had good luck with H. Stern. They have it all and have 2 stores, one in Havensight Mall at the Cruise Pier and one on Main St. Main St is the biggest. ther are few stores that specialize in just gold. However for a fun store to shop that has items in almost every price range try Cardow Jewelers on Main St. Its a veritable supermaket of jewelry. I think its best to shop St.Thomas as the Duty allowance is larger here.
Most of the stores located in St Thomas also have stores in St Maarten. The Exception is Amsterdan Sauer. they are located only in St. Thomas. All three are very reputable.
St. Maarten is better for electronics, cameras, vcrs, etc. Usually about 10% cheaper than St Thomas. You might also try Little Switzerland, located in both places, however their prices are pretty well the same on both Islands.
The ships staff generally hold a shopping seminar on the 1st day out. Try to atend. They will give you good info on reliable shops. They will also recommend specific places but I would take that with a grain of salt as I believe there are Kickbacks involved with their recommendations.
TIP: Have a good idea of what you are looking for costs in your home State or Country for comparison
I have found Omni Jewelers and Cardow Jewelers in St. Thomas to be of high quality with nice, non-pushy sales people. Both are in downtown St. Thomas. Make sure to check out the treasure trove at Cardow. They have deeply discounted pieces they have decided to not carry in their store anymore. I got a wonderful deal there last time we were in St. Thomas. My necklace was about 1/4 of the price I was seeing in the states and of equal quality.
Check out www.vinow.com they might have website links to some of the stores in St. Thomas.