On Grand Cayman the good news is that there's no sales tax and there's plenty of duty-free merchandise. The bad news is that prices on imported merchandise -- English china, Swiss watches, French perfumes, and Japanese cameras and electronic goods -- are not always lower than elsewhere.
Locally made items to watch for include woven mats, baskets, jewelry made of a marblelike stone called caymanite (from the cliffs of Cayman Brac), and authentic sunken treasure. Cigar lovers take note: some shops carry famed Cubans such as Romeo and Juliet, Cohiba, and Partagas brands (but enjoy them on the island, as bringing them back to the United States is illegal).
Although you'll find black coral products in Grand Cayman, they're controversial. Most of the coral used to make items sold here comes from Belize and Honduras, because Cayman Islands marine law prohibits the removal of live coral from its own sea. Black coral grows at a very slow rate (3 inches every 10 years), it is often designated as an endangered species, and reefs are not always harvested carefully. Environmental groups generally discourage people from purchasing coral products.