At the risk of blowing the best kept secret... Go to Rum Point Beach if you're looking for the best beach atmosphere, hammocks, beach bar, surreal Caribbean scenery. You can take a quick ferry over, ask a local where it is, I think it's near the Cruise Port at some hotel.
I did hear that Stingray City was great, After Steve Erwin's recent tragedy, this excursion offering may not be as crowded as it normally would! (kidding)
Grand Cayman, crowded or uncrowded is definately worth getting off the ship. This is definately not an island to be missed. Was there last time with about 6 ships in port, not too crowded, like previous poster said, they handle it well, lots of excursions leaving around the same time but plenty of space.
I don't think I'd go to 7 Mile Beach though with that many ships. That beach was once pristine, now over rated, gets too crowded and too many hotels, didn't think the beach there was that pretty compared to some others I've seen.
Also hear of so many people going excursions to a little town called Hell. I don't plan on going to Hell, I suppose that most people who end up there don't plan on it either. Heard some folks on a cruise complain that Hell was too hot. They really sufferd there, said the tour was long, felt like an eternity. One guy said he was under the impression that it would be fun, some tour operator named El Diablo made a "deal" with him and he ended up getting burned! I would definately never reccommend this place again. I once reccommended it to my ex boss who "fired" me just because I told him to go there!