We rented a Jeep and drove to Rum Point Beach. It was a long drive but well worth it. It's a small beach area, not private but you do get that feeling. There's a long pier, we saw diving boats and party boats docked at the end. A great outdoors bar/restarurant. We had a great lunch and the best Mudslide drinks. Clean and free bathrooms.
Someone told DH that you can get a ferry from one of the hotels to take you there. I sure would like to found out which hotel offers this service, I would much rather cruise there than drive again. Going back there in October.