I spent my birthday at False Cape State Park in Virginia. It was the second time I made the trek into the park and both times were near perfect camping experiences. Due to the Back Bay National Wildlife Refuge bordering the park to the north, there is no car access. This means you can either hike or pedal the 8 miles from the near parking lot to the campsites. This year we took our bikes which cut the trip from over 3 hours to just over and hour. There are 12 sites total split evenly between the ocean and back bay side. While the campsites themselves are behind on the dunes on the ocean sides, you can camp directly on the beach near posts designated by your campsite number. The picture below is no Ansel Adams, however I did like the composition.
UPDATE: I added a video of the sunrise coming on the beach.