Nicole,
I have been on many cruises and from my experience, I would recommend NOT going with the cruise excursions. I recommend going on your own adventure, plus it’s cheaper. The cruises usually set up trips that aren’t very challenging and get you through the activity to collect the money and don’t forget the tip.
With that said, Grand Cayman Island is one of my favorite places to dive. I saw from your profile that you are a novice. What I would recommend here is to dive Eden Rock or at DiveTech (West Bay Location). Eden Rock is located near where the tenders drop you off. Once you get off the tender go to the right and about two blocks away, you will run right into the dive shop. The dive is fairly shallow, but there are some very cool swim throughs and underwater critters. DiveTech also has equipment for you to rent, but will require a can ride or a car rental (which may make Eden Rock a more favorable choice). The pier runs right off the dive shop and you can get in a great dive on a shallow wall. If you want to truly experience a Grand Cayman Wall Dive, look online and set up a wall dive with any of the dive charters. Make sure you let them know that you are coming from a cruise ship and which one. They will let you know if they will be able to accommodate you (make sure they can get you back in time).
As for Cozumel, again there are many dive shops in the area. Simply go to one and rent your equipment and jump in. The shallow reef has taken a beating over the past few years. I’m not sure how well it has come back. But, the last time I was there, it was still hurting. That is why we steered towards more wreck dives. If that interests you, see if they can bring you to the airplane wreck,. It’s not something you see everyday (at least while diving).
I hope this helps! Enjoy!