All 3 of those ports offer good snorkeling. If you are interested in doing Cave Tubing - then that would be done in Belize, and I suggest you use Reggie. I did a special report on that excursion for Port Reviews: http://www.caribbeanportreviews.com/Belize51.htm
You might want to checkout the other information on all of your ports at that site as well.
However, in Belize there are also great snorkeling trips offered by the cruise lines that pick you up directly from the ship (no tendering involved) to transport you to the Belize Barrier Reef for snorkeling (Ambergris Caye, Shark/Ray Alley and Sergeant's Caye are all good).
Snorkel and Stingray City with one of the local tour operators in Grand Cayman is also another good option. I have used Captain Bryan with great success.