Cayman is beautiful. There isn't much to do other than sleep, sun, dive/snorkel, and eat/drink. There is Hell and a turtle farm and there is a golf course. It is very americanized. It has the fast food burgers and I think subway. The is a local hang out for divers and divemasters call Lonestar that has awesome tex-mex food. They used to have a good fudge brownie sundae--MMMMM.
We have stayed at the Villas of the Galleon and loved it. They are condos you rent and are right on one of the widest beaches on one end of 7 mile beach. If you are staying a week, you can save a little money by doing a condo and buying food. It is expensive. Also, I believe they still do the money exchange in such a way that no matter what money you give them, they give you cayman. I haven't been to the island in a few years and that was on a live-aboard dive boat.
Don't forget to try the Tortuga Rum Cakes. They are heaven. I have brought 6 back onto cruises before only to finish off 3 before the end of the cruise.
Enjoy!
DG