You might want to drive almost straight west out of Chicago to go through Galena, Illinois. It’s a cute little town right on the Mississippi. If you continue across Iowa, you could pop in at the Grotto at West Bend, Iowa (a little out of the way, but worth it.)
There are two must-sees on your way across SD if you’re into funky things: The Corn Palace in Mitchell, SD (lame, but amazing at the same time) and Wall Drug (you’d be a fool to not at least stop there after all the signs you’ll see!)
I agree with others that you should at least drive through the Badlands. And make sure you have your camera. Depending on the lighting and the weather you’ll see spectacular stripes in the landscape. You should hit this just before Wall Drug, as it will circle back out and straight into WD.
While you’re in the Black Hills, you’ll see the most animals if you go a little further south than Rushmore and go to Custer State Park. This is the main place (outside of the presidents) that you have to see in the Black Hills. It’s easily my favorite place there. You’ll see more animals on the gravel roads, and whenever you can, ask people you see at other stops if they’ve seen anything really good. They’ll be happy to point out where the big herds are, or where they saw something amazing. They’ll be your best guides.
While you’re in Custer, if you’re into funky, you might just have to hit Flintstone Village. You get Fred & Barney & everyone else, but the oddest things are the places where they cut corners and just painted freaky faces on mannequins and stuck them in the Bedrock Barbershop. Realize you’re throwing your money away, but it’s almost worth it for its astounding lameness!
Devil’s Tower is a good stop back up near the interstate. (visit with the groudhogs) If you have the time, you might even swing a little north into Montana for Little Big Horn, but make sure you hear one of the rangers tell the story. (If you can get the one who teaches in Texas, he was astounding. Made the whole visit there worth it!)
Be prepared for Yellowstone. We’ve been snowed out in June before, so weather is very unpredictable. If you can possibly afford a telephoto lense for there, it’s completely worth it. Binoculars, too. Last trip we saw buffalo, bald eagles (usually at the west entrance/exit), deer, elk, and grizzlies. If you want moose, make sure you go out south all the way to the lowest part of the Grand Tetons.
On the way back to Chi-town, take backroads if you can stand it. The interstates both ways are painfully boring. There’s even less to see in Nebraska than SD, believe it or not. If you really want more, visit Scotts Bluff in Scottsbluff, visit “car henge” in Alliance, get your picture in front of the “Home of the Testicle Festival” sign at the Round the Bend steakhouse in South Bend, Nebraska, and hit the Omaha Zoo, one of the nation’s best.
You could visit the Danish windmill and get old-time Danish meat (rollepolse) in Elk Horn. You could go through Amish country near Iowa City. There ain’t much else along I-80…
Final advice: MUSTSEE: Badlands (quick drive through) and Custer State Park.
We used to live in Chicago and I’ve been to the Black Hills about 6 times, as well as 3 trips to Yellowstone and spending time in western and eastern Nebraska (and growing up in NW Iowa.) We just did this trip last summer, actually.