Fabmommy - please reconsider your thoughts on shore excursions- especially in Grand Caymen- Sting Ray City/Sandbar is an experience for all that should not be missed, all ages can experience this wonder of nature. Book independantly - so many great local tour operators to choose from, that are so much cheaper than the ships shore excursions, you can do it for not much more than it would cost you to get to and from the beach when you add up all the incidentals. We love Captain Marvin for this tour, very informative,friendly and helpful.
Cozumel - you can't get to any of the beaches without taking a cab. Channunkaab National Park is a great place to spend the day, so much to do here- really nice beach with good snorkeling, there is an Aquarium, replica of the ruins, gardens to wander around, sea lion show,- all included with cost of admission $10.00 per person. It is very clean. go to www.cozumelinsider.com
for some great info on beaches, also go back into the articles section of the board and look for Luisa's article on family friendly beaches.
Jamaica - if you want to do the beach thing you really need to go to one of the hotels and buy a day pass. All ages can go to Dunns River Falls, you don't have to climb the falls if you don't want to, there is a walkway all along the falls. You can get there by just grabbing a cab at the pier. Cab fare and admission to the falls is cheap. You can also book an independant tour very cheaply we like Peat Taylor - check him out on his web site - same as his name.