Going south I-95 avoid DC area between 7AM and 11AM and again 3 PM to 7 PM Coming South to I-64 you may want to stay for a night or two in Williamsburg Va. A lot to see with the restored colonial buildings and tours.
Then take I 64 east to US 168 south in Chesapeake to go to Hatteras.
Visit The Lost Colony in Manteo as well as the Wright Brothers memorial and see some hang gliders, they do offer lessons. A ferry trip over to Ocracoke Island.
On your way back since your going to Jersey, take 158 back to Chesapeake, but then take the Chesapeake Bay bridge tunnel, 26 mile overwater trip, and then you can stop in Chincoteague/assateague islands to see the wild horses before going to the Cape May lewes ferry for the crossing of Delaware Bay.
Just some ideas for ya
Happy motorin