We generally hit the more scenic drives, and you're in the best half of the country for that.
However, it sounds like you are looking for more classic Americana than just scenery. It's getting harder and harder to find that nowadays. I remember the old route 66 roads of 20 years ago that were bypassed by I-40 that were interesting but much of those interesting things have dried up and disappeared, unfortunately.
I still like driving the Million Dollar Highway, north from Durango, CO up to Ouray, CO. It's a steep mountain highway and gets narrow in a few spots but we handled it OK in our Bus, pulling a Jeep. The towns of Ouray and Silverton are great stopover places and are loaded with plenty of interesting things, in additrion to drop-dead gorgeous scenery. You'll need to spend some time in them to properly explore the area. There's some nice ghost towns in the area and if you are pulling an SUV, you'll be in great shape. If not you can rent a Jeep in those towns to see the tougher to get to places.