Just made a trip from central Illinois to Houston and can recommend the following:
Hwy 67 from just south of St. Louis to Little Rock
and
Hwy 59 from Texarkana to Houston
Haven’t made this trip for many years, but Hwy 421 used to be a nice route (not quick, but nice) from Lake Michigan (Indiana) to Myrtle Beach, SC
Many, many thanks to all of you for your great suggestions. I now look forward to getting out my atlas and plotting a course. I wasn’t looking forward to this trip but now I’ve regained my enthusiasm, thanks to you all.
I like those little motels along the backroads. And I love to stop and read the local newspapers just to see what’s going on in the real America. I also love those old-time diners. Sometimes I forget how lucky I am to now have the time to take trips without time constraints. 
Sue - Consider reading Robert Persig’s Zen and the Art of Motorcycle Maintenance. Very good book about a cross country trek on a bike, with his son.
I’m a big fan of the diners too. Most times I don’t even look at the menu…just ask the waitress, “What’s good today?” Never been disappointed.
Hospitalized, yes. Disappointed, no.
Wow, I had no idea that 202 went anywhere but NH and ME…makes me wonder where I could get to just from my exiting my road onto 202 and taking no other routes 
It goes almost all the way down to New Castle, DE. It even runs right past the town where I went to middle school: Brewster, NY.
Hwy 34 to Loveland, CO. Go north on 287 to Hwy. 14 north of Ft. Collins. West on 14 up Poudre Canyon to US 40, over Rabbit Ears Pass, through Steamboat Springs, Craig, all the way to Park City, UT.
I’ll wager this section would be the most scenic part of the trip.
