If you would like a wonderful cottage to stay in on Grand Cayman Island, the the Royal Palm Cottage is perfect. This was an immaculate one bedroom cottage with all amenities (washer, dryer etc) located in the middle of Grand Cayman so that it was easy to access Georgetown and 7-mile beach to the west, and the more rural and lovely east end. It was located just near the only road that travels N to S, making it a great central spot, especially if you don't like crowds, cruise ships, and traffic.
The only downside to this location (well, all locations on Grand Cayman really) is that is located next to the only road which is really busy with a lot of truck traffic. You really can't escape this. Just across the road though is a lovely little private beach with shallow water which is perfect for all ages.
The little resort next door has 5 rooms with private baths and is also lovely for larger groups. The managers were very kind and welcoming. The whole setup is clean and nicely decorated. One note, you MUST have a rental car to get around Grand Cayman, and the driving is English on the Left side, so be prepared!