In Grand Cayman there are stores near where the ship docks but I highly recommend that you go to Stingray City...This place is like nothing I've ever seen before. Basically you go out in a boat to the middle of the Carribbean and you come across a sndbar where you get out of the boat (the water is about waist deep) and there are stingrays swimming all around. At first it is pretty intimidating, one swam by me and rubbed against my leg and I jumped onto the backof the guy standing next to me, thankfully it was my brother-in-law, but it is the neatest thing I have ever seen. They aren't held captive there they just come there for the food that the boats bring..you can feed them. It ws amazing! I hope to get back to Grand Cayman soon to take my kids there.
If you enjoy snorkeling the waters aroung Grand Cayman are gorgeous.
Also, there is the Turtle Farm [retty neat. They breed seat turtle and then release them when they are big enough to survive.
Also, Hell....I think that is one of those places that was neat to see once but don't think I would go back to, really toursty.
A couple of years back my DH and I spent a week in Grand Cayman and absolutely Loved it...There are quite a few things to do there.
Let me know if I can help further.....