We dive Cayman a lot. Usually with Don Foster's.
Are you bringing your own gear? If I had my druthers, I'd actually do a shore dive and not worry about the boat ride since you have a time on shore. My first choice would be
Lighthouse point, very easy to get to, basically you head west towards West Bay. It's a gorgeous, shore dive, and much nicer than you'll see on one of the shallow cruise shippers dives.
Or, I'd just head over to Sunset House and do their house dive.
Probably my favorite dive on all of Cayman is the old house reef for Spanish Bay Reef, but the resort is under some kind of construction and I don't know if you could walk down to their dock. It also probably wouldn't be too easy to find.