I would take I-80 to I-39 to avoid driving through Chicago traffic. We went through there at the end of May on our way to Yellowstone.
The waterfalls in downtown Sioux Falls is very picturesque.
If you are towing a trailer or have a toad, here are some suggestions for Custer State Park. Iron Mountain road (Rt 16A) from Custer State Park to Mt Rushmore has 3 tunnels that frame Mt Rushmore as you drive north to Mt Rushmore. On the Needles Highway, the tunnel at the Eye of the Needle is only 8' wide. Both the Iron Mountain road and the Needles Highway have height and width restrictions so they are not suitable for motor homes.
There are several nice waterfalls along the Spearfish Canyon Hwy (Alt Rt 14 south of Spearfish).
If it is too hot, there is Wind Cave NP and Jewel Cave NM near Custer to cool off.
You may want to drive into Montana on I-90 (Crow Agency exit) or take US-212 from the Black Hills to visit the Little Big Horn battlefield.
Rush 19 Toyhauler