We had a wonderful trip to Grand Cayman a month ago. The following might be useful:
Seven Mile Beach (which you will have gathered is pretty much the only place to stay) is a wonderful beach but in many places Hurricane Ivan has taken away the underwater sand leaving sharp rocks which can be tough on the feet: suggest you buy some beach walkers at Diving Supplies (v. cheap and worth it).
Restaurants: Cayman has some fine restaurants: we ate at three: Calypso Grill (a bit out of the way but marvellous food and ambience right on the water, well worth it); the Lobster Pot (as the name implies, excellent for lobster but we also had great snapper and Claudia knocks up a mean Pina Colada); and the Wharf (terrific ambience but the food was not that wonderful).
We had a wonderful day at Rum Point (preferably go on a week day as it is very popular with the locals at weekends)—free sun loungers and a fantastic beach, just great for chilling out.
In terms of diving and snorkelling, Sting Ray City is a must. We used Red Sail, a very efficient and well-organised operation but they tended to go out in the afternoon which was not always the best time (the sea seemed to get rougher). However, we heard good reports about Captain Marvin (who go out in the morning).
Grand Cayman is quite an expensive island but the shopping in Georgetown is good if rather high-end. Nevertheless the town is so quaint it is worth spending a morning wandering around—just avoid a day when the cruise ships are in.
Lastly, the rum cake. Great stuff..