We rented a VW Safari from Less Pay Rentals in Cozumel. Only $38 or you could rent a jeep for $50. We drove around the entire south end of the island. Saw beautiful, virtually deserted beaches on the south and east coasts. Visited the San Gervasio ruins, drove back to the ship for lunch, then took the Safari out again and went snorkeling at Chankanab park. We used our own snorkel equipment. The entrance to the beach is rocky but there are steps built in. And a guide rope to lead you back to the steps. The snorkeling there was beautiful, the beach was quiet and had good amenities, but no pressure. There is a $10 per person admission fee, but it was worth it. There is a trail with replica ruins that look real, and many plants and trees. Very beautiful. There is also a dolphin adventure there and a museum, as well as a lagoon that you can look at that has crystal clear water with many plants and fish. The lagoon is connected to the ocean through underwater caves so many ocean-dwelling fish inhabit and/or visit the lagoon. We visited San Miguel but didn't do much shopping, but there's plenty there to do, and many bars and restaurants. You can also get around quite easily and relatively cheaply by taxi all over Cozumel. (Although we thought it was a better deal to rent the Safari because we wanted to see a lot of the island and have flexibility.)
Grand Cayman is spectaculr. Very wealthy. More expensive than Cozumel. We did the Stingray City half-day tour (3 hours) through Captain Marvin. We were glad we did, because all the cruise ships in port that day (5) canceled their snorkeling and Stingray CIty tours because of rough seas. But the small independents went anyway, and it really wasn't that bad. In fact, I think we were lucky because I can't imagine the crowds if all the cruise ships had sent their tours out. I recommend booking through Captain Marvins and getting on the earliest possible tour. This should beat most of the cruise ship tours. Captain Marvin's is just two blocks from the pier. And it's very safe walking around on Grand Cayman. It reminded us of Hilton Head. Have a blast!!