Bill,
Unfortunately, most of the truly excellent operators in Grand Cayman are on the other side of the island, and are not practical on a cruise ship schedule.
The big operators, Bob Sotos and Don Fosters both do a really good job, but you will be with a lot of other people. Sunset House is a good operation, but emphasizes shore dives. They got beat up pretty badly by Hurricane Michelle last year, but I understand they're recovering nicely.
Easiest location is to go to Eden Rock near the tender docks. Nice shore diving, but there are a lot of people there.
My personal favorite is DiveTech on the West End (near the Turtle Farm). They have both excellent shore diving (a mini-wall to about 70 feet a very short swim out), and boat dive offerings, and they're good about accommodating cruise schedules. They are a bit difficult to get to, as the taxi drivers at the dock don't like taking single passengers (and losing out on a tour fare), but I feel it's well worth it.
While I haven't been diving with them, FishEye on 7MileBeach comes highly recommended by one of my local dive shops in Denver. I've yet to read anything but good from them. The reason I didn't use them this last time was they needed me to be at the shop by 7:45 (I was doing some classes, so that may have been a consideration). They also were the ones who originally recommended DiveTech to me. If you can work out a schedule with FishEye, they would probably be a great choice.
RedSail might be another option for you - I don't have as much information about them, however.
I have the email addresses and urls for all these shops if you need them. I hope this has helped a bit!