I have been to Cayman a bunch of times, and used to stay at the Dive Lodge (for the most part) which was on the East Side. I really prefer the East Side diving myself. Great Walls and off the beaten path, but of course it is relatively far away from the main town.
I keep on meaning to get down there to check out Ocean Frontiers, many people have recommended it to me and it is fairly close to where the Dive Lodge was on the East Side. Cayman is pricey and making some meals for yourself is a good idea if you do not get an all-inclusive (Ocean Frontiers has some things, and I would guess the others do also.) Cathy Church is down there, and she gives UW photo lessons, if you are so inclined.
Even if you stay on Seven Mile Beach/other side of the Island, try to see if you can get a couple of dives in on the East End somehow. Stingray City is a big attraction (can snorkel there for non-divers). Of course you can go to Hell (little spot, kind of fun for the standing joke, we did it on a day we could not dive due to the weather.) There is the Atlantis Submarine ride, the Botanical Gardens and other various attractions.
Trip Advisor has some info Some More Here.
Giles has alot of info on Grand Cayman, so I am sure he can add more if he bops into this thread.