You can always take a cab to the beach. Seven Mile Beach is the place to visit on Grand Cayman. Playa San Francisco is a nice beach on Cozumel and Chankanaab Park is a nice way to spend a day snorkeling and sunning.
If you like the water and you want a thrill, I highly recommend the Stingray City excursion on Grand Cayman.
And there's always shopping at either port.