False Cape State Park -- South of Norfolk between Back Bay NWR and the NC border.
False Cape State Park
I don't know if they still allow it but you used to be able to camp on the beach overlooking the Atlantic.
Do pay heed to the tides if you decide to hike in on the beach. We failed to take that into consideration and had to walk in soft sand of the dunes. It was seemed like a death march compared to the walk in at low tide.