Currituck is cool as it's not a Nat Park and flying there is not restricted - yet.
Hatteras and Bodie are a challenge to make sure you are not on park property taking off and landing, but simply flying in the airspace. Bodie is pretty accessible if you go to the marina down the road from Bodie and fly across the water. Not 100% sure if that is acceptable (did not fly that way) due to the Coast Guard facility right there too. Yet, if you stay closer to the main road it may be out of their space.
I also flew down on Ocracoke to that lighthouse - off property of course - as we went in the summer when ALL the lighthouses were closed. Went back to Outer Banks in October and Currituck had opened to the public - albeit at $10 a person to go up inside.