Carolina Crossroads in NC - just south of the VA border - has sites set aside for late arrivers. I think they're water and elec only. Easy to find, close to I95, nice people running it, although they're only there from 9 till 5 so you probably won't meet them.
One exit north of there is a Walmart with a good size back parking lot area. We stopped there to stock up and the security guy came by to help me park. He asked if we were overnighting, so I assume it's allowed. I don't know if the security guys are there all night.