I was there a few years back for work. Never went diving, but the snorkeling was sweet! Royal Grammas everywhere!
There is one public beach on the south side of the island. Swim straight out from there until you hit the reef. When I was there, it was loaded with black triggers. FYI, this is the only beach, everything else is rock. I was there in August and it was me and the Park Attendent (taking a nap)
Other than that, the whole island is rock bottom. Snorkeling is pretty good pretty much anywhere you jump in the water.
there is one hotel that does (or did) an all you can eat steak and lobster night. I think it was Wednesday. Ask about any local, they can tell you which one it was. South side of the island by the airport is all I remember.
Make sure you hit some of the caves while you are there and go watch the sunrise from the lighthouse and sunset from the "beach" on the west end of the island (facing Little Cayman, not the beach above). The "lighthouse" (you'll understand the "quotes" when you see it) is on top of the cliffs. You can drive right up to it. Super cool, but watch your step!!! Rocks are extremely sharp and it's a long way down!
Awesome place to visit, but I'll never go back for full week again. 3-4 day weekend is good for me. Not much there.