The Rockefeller family operates a large cattle ranch on he island. We used to pick up a mooring in Galley cove and follow the path up from the beach. Eventually that path intersected a road and we walked all the way down to the ranch. I don't believe they encourage visitors but the family who ran the ranch were gracious and courteous, introducing us to a mama steer (I guess they are called), which was the size of a Volkswagen bus. The family seemed to be from the plains states and spoke with a definite Texas or Oklahoma twang, addressing my wife as "..yes'm..., no ma'am...". Wonderful folks. They also have moorings down in the narrows where their main dock was, although they very much discouraged picking up one of their moorings. Good times.
PS Tom: While writing this it occurred to me that my comments above are on Bartlett Island, just east of Long Island. I do remember on Long Island there is a beautiful beach down at the south tip where we often saw boats anchored to enjoy the beach. Other than that, I had no experience on Long Island at all. Big mystery.