You can't camp on them. North of Duck is Corolla/Carova and the beach is highway 12 and busy this time of year. No camping and they patrol for it. You have to have an off road permit for Hatteras and there is no camping and it is enforced. You can camp on Portsmouth Island but it is accessible only by private ferry from Atlantic, NC (not in OBX). http://portsmouthislandfishing.com/portsmouth-island-nc-ferry.aspx
That ferry can take your vehicle. The ferry from Ocracoke (OBX) is for pedestrians. Somewhere, I think Expedition Portal, a guy has a thread about camping on Portsmouth Island. It's an abandoned town and belongs to the government now. If you go you have to post some pictures!

 

I also recommend Assateague Island, just south of Ocean City MD. You have to buy a permit to drive on the beach: https://www.nps.gov/asis/planyourvisit/osv.htm

 

This is Assateague in the 70's. Pony bottles and bad haircuts. I had a cooler like that one but mine was harvest gold.

 

That is a classic photo!
Would make a good album cover.

Regarding the beach driving, New England doesn't offer much.
Nauset beach on Cape Cod(best bet) and Martha's vineyard have limited areas and the price of entry is high.
RI has one beach, south of Boston are Plymouth and Duxbury(aka "bux bury", "deluxe bury") and iirc Plymouth is extremely restrictive(residents only)
Nantucket has a drive on beach, but they don't want you to bring your car to the island. So you can rent Jeeps there and drive on for a fee.
NH has nothing.
The coast of Maine is probably too rocky.
Camping on the beach in MA is a whole different problem with even worse fees and restrictions.

 

Nervo19, looks like they may need some help getting out of that spot.. haha. Cool picture!