I don't know of any hotels but I know there is public areas where you can use there showers and restrooms free of charge. Seven Mile Beach is a very nice place to visit. Very clean. Stingray city is another great adventure to do while in Grand Cayman. We will be there in Ocotber and going to do Stingray city.
Hey Charley,
We will be there in October too. I'll be booking the stingray tour with Captain Marvin's, and probably spend a few hours at 7 mile beach.
San Antonio Bill, they may let you use their facilities if you say you're looking for a place to spend a week for your next vacation. Sometimes just blending in works. You don't do that by carring a ships towel.