If time is no limit, and your rig is appropriate, the route I like is Smokey Mtn NP, then the length of the Blue Ridge Pkwy, then east to Cherry Hill in DC, from there the Philadelphia, NY, Boston area for history and sights, then on to Maine. On the way back vary the route to see things like Amish country in Pa, Gettysburg, LuRay Caverns, Ashville,NC , or coastal areas like Savanah, Hilton Head, Myrtle Beach, Charleston, etc on the way up or back. I make this run to/from Maine every summer and this is just a partial list of points of interest. In Maine, you could start with Old Orchard Beach, Portland, Freeport(LL Bean) BoothBay Harbor, Camden, then Acadia NP. Cadillac Mtn is the highest point on the NE coast. Further north in Maine Quoddy Light near Lubec is the farthest point NE in the US. Further inland in Maine Baxter State Park is the terminus of the App Trail, Moosehead Lake is a few miles south. Moxie Falls and The Forks all scenic wilderness areas of pristine lakes and streams. And in the NW corner of Maine is the Allagash River wilderness area. This is just a partial list of places I have visited in Maine and along the way. Others can add many more. Go to the library or Barnes&Noble. Lots of good travel guides with suggested routes are available for each area of the East Coast.
Order is illusion. Chaos is reality. But right or wrong I'm still the captain. ๐