Splendid Nature is Easy, Interesting Towns are Even Easier
Velkommen! Welcome aboard the RoadTrip America Forums!
Let's start with the only downside to your itinerary. You really don't have 13 days for your cross-country drive. With a day to get over jet lag in San Francisco and a day devoted to getting into Chicago, dropping off the rental car, getting through security and boarding your plane, you really only have ten or eleven days to devote to the RoadTrip itself. Still, that's fine since the routing I'm going to suggest (and will hold true pretty much whatever reasonable routing you eventually end up with) will take about five and a half days of driving. That will still leave you with five and a half days or so to devote to out-of-the-car activities, a good mix.
So, for some 'splendid nature' stops: From San Francisco head east on I-580/CA-120 to Yosemite National Park (NP); continue through the park over Tioga Pass to US-395 south to Lone Pine CA and CA-136/CA-190 through Death Valley NP; then head for Las Vegas (as American as anything else you'll see on your trip). Next head north on I-15 to UT-9 and Zion NP; continue to US-89 north and UT-12 east to Bryce Canyon NP, then return to US-89 north to US-70 east and US-191 south to Arches NP; use UT-128 to return you to I-70 over the Rockies to Silverthorne CO and take CO-9 north to US-40 east and US-34 into and through Rocky Mountain NP; continue out the park on US-34 to I-25 north to Ammon WY and take US-18/SD-79/US-16T north to the Rapid City area. Now there's a lot to do around there including Mount Rushmore, Wind and Jewel Caves, Devils Monument, and the Crazy Horse Memorial. When you're ready to move on, take I-90 east past Badlands NP and on through Minnesota and Wisconsin to Chicago. As you can see, such a routing gets you plenty of 'splendid nature'
And as for 'small towns in odd places', that is (as noted) even easier. For those stretches of your journey where you're not on the Interstates (motorways), you'll mostly be on two-lane trunk roads that will take you directly into small towns and through ranches, forests and farms. On those stretches where I've suggested Interstates, you can often drive parallel roads that let you do the same and give you the option of using either road depending on whether you just want to drive for distance or want to take a more relaxed attitude. The best example would be near the end of your journey where, if you still have time to spare, you might want to use US-14 instead of I-90 for parts of it.
AZBuck
Some more along the same route.
Near Badlands, you will come to a small place called Wall. There is a very touristy, but none the less interesting store with a lot of history. Be sure to stop, even if you do not fall for their souvenirs and clothes you probably don't need.
Get your 5c. cup of coffee and your free iced water - and be sure to learn the history behind both of them. Same with the Traveller's Chapel. Then as you move to the backyard, take a little time to read some of the history displayed there (on the wall) and also the many artifacts and historic machinery.
Then before you get to Sioux Falls, there is Mitchell, where you will find the Corn Palace. This too has a lot of history of the farming in the area, with corn used as their palett to create their history in pictures.
Further on, in Minnesota, take an opportunity to leave I-90 at Dexter. MN-16 here will take you to Preston, and then continue as the Historic Bluff Country Scenic Byway, to the Mississippi River. At that point you can either head north back to I-90 at La Crescent, on the MN side of The River, or from La Crosse on the WI side.
Places you will pass through are varied and interesting, and from memory, most are of fewer than 2000 people. In one, forget which, (it is some time since I was there), there is a Norwegian coffee shop. There are also quite a few short side trips along the way.
Lifey