So take 81S to 64E and hop on the Richmond Bypass (295) till it hooks back on to 64 east. That will bring you to the Williamsburg KOA.
From there you can continue directly on 64 to Va. Beach turning on 264 IF you are less than 13.5' which is the clearance in the Hampton Roads Tunnel. I go through this with my ClassA at 12.5' all the time with no issues and no inspections ever...though I suppose it could happen.
If you are over 13.5' you need to hit I664 toward Newport News and go through the Monitor/Merrimack Tunnel and will then bring you back onto I64 and you can hook up with I264 to Va Beach proper.
These are easy interstates and should be relatively stress free for driver & navigator!
There are only 2 campgrounds close in to the beach...KOA & TravL park...suggest you get on the phone if you want a spot at either.