I wish we had a week to spend in Grand Cayman! For $35 you can do an organized tour to Stingray City plus one of the reefs to snorkel, which includes equipment, stingray food, your sailboat ride, and more. http://www.cayman.org/crosby
is one site for such a tour but there are many others that would be similarly priced. Booking through the ship will cost you about $75 for the same excursion. If you don't care about seeing the stingrays though (or in my case, don't want to bring my 2 yr old on that excursion) you can snorkel off the shore. http://caymanislandsdiscounts.com/Of...Snorkeling.htm
has great tips about locations and where rental equipment is available, etc. There are many good locations that would be just a short taxi ride or possibly even within walking distance from the ship. Good luck!