Ahh, home. I used to drive that route several times a year. How long will you be traveling? When are you going? If you are going in August I hope you made reservations a looong time ago! With the Sturgis bike rally in early August you will not find places to stay. It can be impossible to find places to stay anywhere between Sioux Falls and Yellowstone.
Coming across Minnesota stop at the SPAM museum in Austin. It is a really fun place. Just before you hit the South Dakota border you can hear a little north off of 90 to Pipestone. There is a cultural center there where you can see a quarry where they mine pipestone. There are often Native American artists there carving the pipestone.
Sioux Falls is a fun city. The falls are very cool. (My daughter wants to go to college there just because of the falls.) They have a very nice science museum in the old Washington High School downtown. They have a cool downtown.
The World's Only Corn Palace in Mitchell is kind of a fun stop. Not quite as big a tourist trap, but almost. There is also a place in lMitchell where kids can help at an archeological dig. I can't remember off the top of my head what it is called.
In Chamberlain there is a very nice Akta Lakota Museum about the Lakota culture. I taught at the school there and the museum was one of my favorite places to visit. The American Creek Campground is pretty nice. Definitely stop at Al's Oasis on the west side of the Missouri River. It's a great place for a buffalo burger and homemade hot apple pie with cinnamon ice cream!
I've never stopped there but there is an 1880s town that I've heard good things about.
The Badlands are beautiful, but it is a long drive through them. There is some hiking, but it isn't easy hiking. You have to be very careful about heat exhaustion, rattlesnakes, scorpions, loose rocks. It's a long way to a hospital. An acquaintance of mine broke her ankle while hiking there. They had to carry her out about 3 miles and then drive to Rapid City. It was took several hours to get her to the hospital. Hiking would be fun, but be prepared!
Wall Drug is the quintessential tacky tourist stop! Fun place to stop.
There is tons to do in a Rapid City and the Black Hills. The Journey Museum is really good. Reptile Gardens and Bear Country USA are ok. My kids loved both of them. I think Bear Country is a little over priced. If you want to see some incredible Native American Art then stop at the Prairie Edge in downtown. They have statues of all of the presidents in downtown and some nights they have live music in the square downtown.
Mount Rushmore is great to see both in the day and at night. Although Crazy Horse isn't completed yet it is a fun place to visit. Check to see if they are doing any night blasts. (A good book to read with your kids about Crazy Horse is called In the Footsteps of Crazy Horse by Joseph Marshall III. It will help them learn the significance of Crazy Horse in Lakota history.) Keystone is a fun little town to walk around in. So is Hill City. Personally, I don't know if Deadwood is all that great if you aren't going to gamble. In Lead I think you can still tour a gold mine.
We did a road trip out there a few years ago and ran out of time to go out to Custer State Park. That same year some friends of ours camped out there for a week and loves it--chuck wagon dining, horseback riding, hiking, buffalo, and other things. Needles
Highway is a cool drive.
Spearfish has a fish hatchery that is fun to tour. Spearfish Canyon is beautiful.
The trip to Devils Tower is a nice side trip that would take a good day to do.
Do you mean you are going to take I-80 home? It would be faster than I-70. If you take I-80 consider driving down to Ft. Robinson, Nebraska. It's a neat historical site with lots of camping. (Big connection to Crazy Horse.)
Let me know if you want more details about anything.