We've driven from NJ to South Carolina, Virgina etc. Depending where I'm going I either take the Chesapeake Bay/Bridge Tunnel and go up the Delmarva or go the more inland route and take I-81 to I-78 into NJ. The roads and traffic around DC are something that I don't enjoy and avoid.
This time of year watch the weather, 81 in the mountains can be interesting. If you take the bay/bridge just make sure your propane is OFF, they do have a pull-out area and will ask. There is a nice big rest stop at the northern end of the bridge where you can stop and turn it back on and rest if needed.
I forget the exact details but some of the tunnels on 95 through DC doe NOT allow propane and you have to go around. Tolls and roads I found stressful.
Drive safe!