If you're on I-90 near Mitchell SD, that's where the Corn Palace is located.
http://www.cornpalace.org/ Just down the street is the Enchanted World Doll Museum. (adults $5, kids 6-18 $3)
The big car museum is in Murdo SD, also on I-90.
http://www.pioneerautoshow.com/ It is spread out in many buildings, not very fancy but there's something for most people to see. (adults $8, kids 6-13 $4, the webpage has a coupon)
If you cross the Missouri River in Chamberlain - Oacoma, stop at Al's Oasis for the apple pie with cinnamon ice cream. (or whatever your favorite is) It's something to do at least once. They have a noon buffet too.
In Rapid City there is the Journey Museum. It is about the people who traveled to South Dakota, as well as the native Indians. Lots of artifacts, photographs, and even some holographic images of people projected in places where you can sit and listen to what they have to say.
http://www.journeymuseum.org/english/ Downtown Rapid City has lots of brass (?) statues of presidents and other statesmen from American history. You could take your picture with Nixon!
Now, when you're at Mount Rushmore, go into the museum part and look at the exhibits. Here's a hint: there is a plunger like they used to dynamite the rock when they built the thing. If you push it right you will get the explosion to go off on the screen and the loud boom to go with it. The trick is to pull up the plunger, then slam that sucker down as hard as you can. It should explode. Not every one can get it to work, you'll have people flocking around you wanting to know how you did that!
We saw bison, prong horns, burros, prairie dogs, and regular deer too at Custer State Park. Make sure you take food along for yourselves, as well as water. It's a big park and you can spend hours there.
There's a lot of places around the state that serve bison, check the menu!
Stop in one of the rest stops that have a travel center or kiosk. The state maps are usually free here, and there are loads of brochures to pick up.
Oh, and if you've never been in a cave think about doing that too. Bring long sleeves, they can be cool. Have a good time!!
bugstabber