Delaware Seashore National Park in Bethany Beach, DE. It is a 3 minute walk underneath the Rt 1 bridge over the Indian River Inlet. No trees or pool, but a nice playground, level and large sites, nice facilities. Close to Bethany, Dewey and Rehoboth beaches if you want to go into town.
The sites on the north side of the river are only 1 year old and very nice. The beach on that side is usually not crowded at all, though there is public parking (for a fee) on this side. The sites on the south side were renovated 2 years ago and are pretty nice, but not quite as big as on the north side. The beach on the south side is more crowded. There is a larger parking lot (again, for a fee) and public restrooms.
Camping at Delaware Seashore State Park, Rehoboth Beach, Delaware