I actually found that the jewelry on the ship was very competitive and bought several pieces (we were on the Inspiration). Shopping in Grand Cayman is very high. The best buy I saw on pearls and silver was in Cozumel. Hope this helps.
Celebrity Century 1/09
Carnival Destiny 10/07
Carnival Destiny 9/06
Monarch of the Seas 3/06
Carnival Inspiration 8/05
Carnival Miracle 4/05
Carnival Inspiration 4/04
Sovereign of the Seas 4/03
I bought jewelry from each port you are going to. I bought two Movado watches from Grand Cayman. The prices for the Movado watches are set so the guy told me they weren't negotiable. I paid about half price for the two watches since I bought his and hers. I bought two rings in Costa Maya that were gold and diamonds. Then I bought a ring in Cozumel that was gold and tanzanite. They are pretty much the same stores in both ports in Mexico. I bought them both at Diamonds International. I do buy quite a bit of jewelry so I feel I know how to negotiate somewhat. I took them to a local jeweler to be appraised and he said that 2 of them were worth what I paid for them and one of the rings I bought in Costa Maya was worth about $50 more then I paid for it. I was a bit disappointed. I'm somewhat hesitant to buy the next time I go away. I really thought since I was in a different country I'd really be getting a bargain, but I found out otherwise. That was even going back and forth with them on the price. I feel if I'm paying the same price as I would at home why not buy it at home. It really helps to know what you are looking for and know how much the item sells for.
I bought a white gold, emerald and diamond ring in Grand Cayman. We live in the UK, so I don't know how America's jewelry prices compare to that. But I can tell you that I had it valued for between 2/3 more than I paid.
unfortunatley none of your islands are "known" for their jewelry deals. You really have to watch the quality when you buy. Cozumel is probably your best bet, you can buy loose gemstones here and you don't declare them as jewlery -customs considers them "rocks". Vendors are very aggressive they have people out on the streets that will try to lure you into the jewlery stores. Your best bet might be the end of the cruise clearance sales on the ship.
Don't think that the silver jewlery with "tanzanite" stones are real tanzanite. The "tanzanite" is lab-created, basically purple cubic zirconia. One of the women on our ship paid $250 for the same ring I paid $40 for (I knew it wasn't real tanzanite and laughed at the $238 I was quoted when I asked the price.)
I haven't heard of any problems with tanzanite purchased that was set in gold.
When buying silver in Mexico, always look for the 925 or 975 stamp. That being said, I once asked a sales person in a store in Puerto Vallarta if a piece was ral silver and they sure, of course. I then asked why it wasn't stamped and he said "oh, you want it stamped?" and proceeded to take out some instrument and stamp it! Buyer beware!!