We stay at Delanera. It's on the beach and has full hook ups. There is a state park on the beach but no sewer. They are both on the west end. There is also a new park on the east end that is on the beach. It's supposed to be very nice also. I believe it has a pool. I think it's called the Sandpiper.
I can recommend both the state park and Jamaica Beach. As stated, no sewers at the state park, but they have a dump station of course. Also, half the park (and campground) is on the east side of the island, and half is on the west.