S.H.
As far as I know there is only one--down by the harbor on the other side of the island. It's a small patch of land near the water and you can watch the boats. The beach is on the other side--I can't remember if it's a short walk or not. The air was SO humid, and even though there was a breeze in the camping area, we drove all over the island looking for a hotel after our first night there in the tent. I don't remember any kind of store near the campsites or BBQ grill or anything, I think it was the primitive kind. There was another area near there that took trailers, so if you could get a site there with water then you'd be better off.
Here's the fancy camping ground: http://www.southpadrekoa.com/