I don't believe there is any camping on the beach with swimming. There is a campground, Sara's Campground, right before you come on the Isle.
Lisa is correct. No camping or cabins in the State Park. Sara's offers campsites, no cabins. Many motels/hotels less than a mile away. Beaches close at sunset. You may drive around the park until 11 PM.
No cabins on the beach
Thanks! Your answer is awaiting moderation.