Without time constraints and willingness to take local roads, the options are wide open. It depends more on your interests and how 'local' of a road you can handle.
For example when we visited Virginia some years ago I used some geology field trip guidebooks, and ended up taking some rather minor roads (in a pickup). And also use Road Food to guide use to local biscuits and ham stands. On the return trip west (to Chicago), I chose roads through the heart of Dolly Sods. I also made a point of passing through a couple university towns (Bloomington IN and Columbus OH).
When I lived in Chicago and vacation further west I preferred to take freeways on the lest scenic areas, in order to have more time in the scenic mountains. Still I'm a sucker for rivers and lakes. State parks and wildlife reserves are often located on those.
Others talk of enjoying farm lands, cow feedlots, and slow small town streets (and local museums). Or historic ice creme parlors and burger stands. Seems the antique hunters just cruise the backroads with the intent of stopping where ever something catches their eye.
My approach is to learn what I can about points of interest, make a general plan, identifying critical spots (campgrounds that need reservations, special events on certain weekends, etc). Then just head out, modifying plans as you go. You may find, for example, that after a few days you've seen all backwoods hollers that you want, and choose to take a turnpike till you hit the flat cornfields of Indiana or Illinois. Or choose to meander north along the Mississippi before turning west.