It depends what you are shopping for Jamaica has great blue mountain coffee $16-$18 lb I think it is the best (Sells in the states for $50-$60 lb) Caymans has more shopping than it used to but does not compare to St. Thomas. Cozumel Kahlua - $8.95-$10 liter & Pure Vanilla Extract ($10 QT) Gold you have to shop around for I paid $9-$10 gram You can get perscription drugs in Mexico without a perscription sometimes you have to go to one of the pharmacies more in the shopping area.
None of these ports are really shopping capitals of the Caribbean like St. Thomas, St Martin or Aruba. Grand Cayman has about one long street of ok shopping, but more the tee shirt type stuff . Nothing in particular is going to be cheap or notable their.
Cozumel - you can get good buys on Mexican silver, onyx pieces such as candle sticks and chess sets and those woven cotten rugs . In Ocho Rios there should be places to purchase rum, jewelry and souvenirs as well as the coffee mentioned above.
These ports are much better beach , snorkeling and water stuff ports than they are shopping ports. Regardless, have a lot of fun.