Another possibility is US50/US301. From the Tappae Zee you can head down I-287 and pick up I-95 in central Jersey, across the Delaware Mem. Bridge and join US301 via US13 and US40. The worse part of this way is the Gov. Nice bridge where US301 crosses the Potomac.
Stay on US301 until it crosses I-295 in Richmond and take that to I-64 through Norfolk. If you're continuing onto OBX, take 168/158 down the Currituck Peninsula, then cross over to Kitty Hawk and take 12 down the barrier beaches.
Places to stop... South Philly KOA in Clarksboro NJ right off I-295 (formerly Timberlane). They are set up for one night transients.
We liked the KOA in Fredricksbirg VA as well.
Several campgrounds around Williamsburg.
Jerry & Jeanne
1996 Safari Sahara 3530 - 'White Tiger'
CAT 3126/Allison 6 speed/Magnum Chassis
2014 Equinox AWD / Blue Ox