There's a bunch of good stuff to do in these ports...
Ocho Rios - the biggie is to climb the Dunns River Falls. We did that our first cruise, along with a ride to some botanical gardens. On our last cruise, we did the White River inner tubing and my son did the canopy zipline adventure. Both were excellent. A tour not offered on the ship (but it is offered in the port) is a tour of Bob Marley's house, which would be neat if you're a reggae fan. If you ask nicely, I hear they'll also show you Bob's ganja fields...
In Grand Cayman, you should stick to a ship's tour as that way you won't miss the boat if your tour is late returning (all ships must use tenders). The Stingray City sandbar is the highlight here. The Turtle Farm is pretty neat. Hell is just a post office and a geologic formation, but it's fun to send your friends postcards from Hell. There's an Atlantis submarine (my son loved his ride on the one at Cozumel) and there's even a deep-diving sub that can take two passengers down 1000 feet.
Cozumel was pretty ravaged by Wilma and it's not all up and running yet - for instance, the dolphin swim at Chankanaab Marine Park isn't ready. On our first visit here, we took the Tulum tour and it was pretty awesome. On later trips we've been to the Xel Ha eco park, ridden horses, and done some diving.
Diving is popular in every port, so if you have any interest, get a PADI Scuba license before you go.
There's further details and photos on my web site at www.mycruiseadventures.com