Martha's Vyniard is an island right off Cape Cod. It's even more expensive and more exclusive then the Cape.
A tip, every year in July-August every president in my memory comes with his family to MV for summer vacation. At that point the island basically becomes impassable, especially in the direction of nude beach: secret service is everywhere, roads are blocked off routinely and so on. Three-four years ago I was there when Obamas came. What a traffic nightmare! But... you may end up seeing some of them walk around.
My female friend and I were in a small variety store in Manemsha when Billy, the Bubba with an impressive entourage walked in. Now my friend is very good looking and with distinct foreign accent and that accent gave former pres an opportunity to ask her a series of questions above and beyond "How are y'll doing here?"

Both of us were under distinct (but granted, maybe erroneous) impression that if it wouldn't have been for the secret service folk we would've had a fascinating story to tell when we returned home, which she would've been telling her children and grandchildren for decades to come.
Nude beach is located on the remote, less touristy part of the island called Gay's Head. It's under beautiful clay cliffs. We still have pictures of ourselves covered in silver clay, red clay, and yellow clay. The swimming is not the best on the island (nothing in Mass can beat the sand of the South beach on the other side of the island), it's kind of rocky but if you aim your phone in any direction, you'll see people ducking under the boulders.

Most of the men on the beach seem to walk around, most of the women seem to be lying on the sand, sunbathing.
What else... Oh yea! Be aware of dressed men. If a man kept his shorts on the nude beach, chances are he is not there to enjoy himself but rather a voyeur, and a very uptight and unhappy voyeur at that too. There aren't many of those there but there always some. They look at you funny, some of them can get aggressive. Speaking from personal experience here.