In Key West, the further up Duval street you go, away from Mallory Square, the better the shopping is. More little boutiques that are less touristy and more local/unique artists. Also a few outlet stores, e.g. Coach has an outlet store in KW. Like any outlet, sometimes they have great stuff, sometimes not so much, but worth a visit.
Key West has a few stores youll find in other ports (Little Switzerland, Del Sol-color changing stuff, etc). There are also many fun and whimsical places as well. If you have pets, the Blue Cat has some fun stuff (there are many stores catering to cats thanks to Hemingway). Its in a little mall next to the aquarium. Theres also some sponge/shell stores in the little open market area of Mallory Square. For some different jewelry I head to Whitfield Jack's. Ive bought several items from him. The stuff in the store is not real-he will custom make your items and ship them to you in a few weeks. He has a website if you want a preview of the items. Next door to him is a great little Key Lime Store (cant recall the name though Kermit is the owner). Tons of key lime items are available-candy, pie, juice, sauces, etc. Theres Margaritaville down on Duval (not a short walk) if youre into Jimmy Buffet. Theres also a Birkenstock store that way (if its still there). Also, there are some great restaurants. Just ask the locals and they will steer you to some great places (some off the beaten path)!
i've been to nassau twice - once on a disney cruise and once on an rccl cruise. the silver is usually pretty good and my mom and i have always left the island with quite a large amount of silver jewelry for decent prices.