I think the best thing about the northeast is the nature and especially the coast. If you're going to drive, you should visit the white mountains in NH and maybe do some camping. It's legal to just camp in the woods for free there.
Coastal Maine is very touristy but nice, Portland is a little city with a surprising amount of stuff, and all the little towns to the north of it are pretty. Acadia National Park is nice solely on the off season when the crowds are less.
I like the Champlain region on Vermont and NY. In a car it's fun to take the ferry across the lake to Burlington. Also, you can visit John Brown's original farm house in the Adirondacks nearby, which is imo more interesting than Harper's ferry.
You could also ditch the car and take the train between cities. The Amtrak goes all the way up to Maine. But this does make it harder to really get into nature.