The beach just off our boat looked like something from the Rivera with the changing tents. We had it to ourselves, it was after labor day and closed.
We took a day and brought our folding bikes onto Chappy and traveled the one road that goes through it. It was a hot day and a longish ride. Very interesting island to see. Very quiet.
I give Mass. very, very high marks for public access. You can land a dinghy just about anywhere in Edgartown, and walk ashore or sit on the beach.