My friends who will be travelling with us asked me if I could ask you all about scuba off the Grand Princess. We will be stopping in Belize City, Belize, Costa Maya, George Town, Grand Cayman & Cozumel. They'd like to know where the best scuba is to be had and who is the best to have do it? They would like to avoid using the cruiseline tour.
There is really great scuba diving in Caymen and Cozumel. On Grand Caymen all you need to do is to go to any of the many dive shops that line the warf and sign up for a dive tour. You need to be certified and have your PADI card with you. Lots of shipwrecks in and around Caymen.
Cozumel great diving at the reefs - would consider booking a ships tour here because it takes a bit of a boat ride to get out to the reefs and if something should happen and you don't make it back before the scheduled sailing time, they will hold the ship until your excursion returns, if you book on your own, you could be waving good bye to your ship.
Talk to a local dive shop in your area, i bet they would have some great suggestions as to where the best diving would be at any of the islands.