Grand Cayman, large island, do not recommand to take cruise program, more expensive. Get off ship and there are many local guide/program for you. I recommand to go semi-submarin - boat with deep underwater section to see sea bed, fish, etc through windows. Rest of time walk on the street.
Cozumel, small island with "Sun" shape road cover whole island. Very natural and too natural, not much to play. Do not take ship program, get off ship, find a taxi driver, US$60 will take you cruise whole island, stop to take a snap shot whereevery you like. Finally ask driver to drop you off at public sand beach, which is side by side with paid beach if through ship program. ?? Maya Beach. Eat seafood soup there, very good and not expensive. there is a small outdoor pool under shade. At the end, $10 grab another cab back to ship.
Remember to buy a Mexico hat.
Happy trip.