Carolinagirl,
There are lots of excellent places to stay on Grand Cayman. It just depends on what you want to spend. My family has been to Sunset House 3 times in the last year.
http://www.sunsethouse.com/
Other places have already been mentioned, but decide if you want just boat diving, or boat and shore diving available, meal plans, and how much you want to be pampered.
I have made about 20 trips to the Cayman Islands over the years and just keep going back. I am already looking forward to the next time.