You need to define fall. It comes earlier in Maine than it does in VA.
Campgrounds generally close by Columbus Day.
Plenty of great things to see and do and you could easily spend April thru October and not see it all. IF you like history, nearly every town and city has history.
Suggest you start researching each state and major attractions now and then plan your trip. Narrow you scope of activities to fit what is most important to you.
Also consider that once you are off the interstate system, speeds are subject to the hills, turns, etc. Not wide open as the western states.
Hills generally not as steep as you will find west of the Mississippi except in parts of WV and VA.