Be sure you know the color, cut and clarity you want. Often, when shopping in stores on the islands, they will steer you to stones that are quite inferior. Make sure you ask to see the stones through a jeweler's loop. This shows them that you know what you are looking for. Ask if the stone is certified and ask to see the papers.
A good idea is to shop in bigger stores that handle quality stones before leaving and get an education on what good stones look like. Here in the east (NJ) we have several jewelry exchanges as well as stores like Fortunoff (which carries quality stones). I suggest you use these kinds of places to learn about stone quality and what you are looking for when you look through the loop (inclusions, carbon spots, etc.) as well as identifying color. Then, when you go into the stores on the islands, you will know what to ask for and what you are looking at and can be more assured of not getting ripped off.
We will be cruising the east on November 30 so I hope to be able to check out a few pieces myself.