On Grand Cayman the good news is that there's no sales tax and there's plenty of duty-free merchandise. 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, though the latter is never cheap. Cigar lovers take note: some shops carry famed Cuban brands, but you must enjoy them on the island; bringing them back to the United States is illegal.
Although you can find black-coral products in Grand Cayman, they're controversial. Most of the coral sold here comes from Belize and Honduras; Cayman Islands marine law prohibits the removal of live coral from its own sea (although most of it has been taken illegally). Black coral grows at a very slow rate (3 inches every 10 years) and is an endangered species. Consider buying other products instead.