Are you looking for someplace nice but a bit more economical just for one night? Take a look at the Comfort Suites at the link below. It is on 7MB next to the Marriott, but you have to walk a short path to get to the beach, but it's on the same side of the street and not far. You can see it in the video at the link below.
Their section of the beach is small, but just fine for a short stay, and a daily hot breakfast is included with your reservation. It's a short cab ride from the airport. We stayed there for a couple of nights before getting on the Cayman Aggressor.
Comfort Suites is in easy walking distance from some places to eat and drink. Coconut Joe's is across the street and it is also near to Craft, a microbrewery place if you want something a little more upscale and air-conditioned.
There's also the new Margaritaville Resort, it is located in West Bay where the old Treasure Island Resort used to be, but I don't think that it has beach access (not sure). I have never stayed there but they may be giving a special rate because they've just recently opened. It might be worth checking. When you ask the cab driver to take you there, don't get confused with the Margaritaville restaurant in George Town.
Sunshine Suites is owned by the Westin and it is across the street (across West Bay Road - a busy street) from the hotel. It's next to the Ritz Carlton's west building. Sunshine Suites charges a daily resort fee but that gives you access to the beach and all the amenities of the Westin. The onsite Sunshine Grill is a popular, casual place to eat.
We are heading back to GC and LC in Oct/Nov so please post a report about your trip. I hope that you have a great time!
Grand Cayman Comfort Suites & Resort
