We have done quite a bit of shopping on the Eastern...and we have purchased more on St. Maarten. One of our favorite shops is DK Gems. It is run by a brother and sister...the brother is Raj and the sister is Deepti. Both truly wonderful. We walked back in after a few years of not being there...they remembered exactly what we had purchased AND our names! I had left the jewelry in the safe when we went ashore, so it was truly their memories! I also had worked in a jewelry shop state side for about 5 years so I did have a good idea of what we were buying. Do your research BEFORE you go, it will help a lot! Don't get caught up in the hype...look for quality. In doing your research go to a local jeweler, not a big chain. Look to see if they are GIA certified. This will help.
On Western, Cozumel is fun for silver...and Grand Cayman is good for your gemstones and watches. Columbia International, and DI are good...but they are definitely big chains. Good luck and happy hunting!!!