My first advice for this time of year is to pick a campsite in VA or whatever a make a reservation. This time of year with high temps they may book out in advance.
Not sure time you have for trip, but for towing a long trailer you'll be better off avoiding the DC-NYC corridor. I live in the middle of it and it's a PIA to get around big cities. People Northbound, many follow 95 right in downtown Washington cause the GPS is confused.
If you have some extra time you can follow I 81 into upstate then PA head east to NY/VT. It's Blue Ridge Mountains (Appalachian) but no serious hills cause it's interstate highways. Beautiful scenery
Otherwise use the city bypasses ie 295, 495, etc. In Baltimore the two interstates 95 and 895 prohibit propane tanks in the tunnels, therefore you must go east to the I -695 bridge. Enjoy it, I've skied and camped there, beautiful this time of year.