Grand Cayman is the best spot for the Atlantis dive. This is the next best dive area in the world after the Great Barrier Reef. However, if you have never done the Swim with the Sting Rays, that is a not to be missed excurision and only at Grand Cayman.
On Cozumel, just take a taxi To Mr. Sancho's beach. No entry fee, refreshments and food available as well as rental of watercraft. Plastic chairs are available with rental of padded lounges and umbrellas there too. Go back to the ship for lunch, then into town for refreshment at Poncho's Back Yard. Don't miss it.