We live in Rockford, which is at the junction of I-90 and I-39. We have gone to the Black Hills twice from here. I-80 to I-39 is way out of your way. A better route is I-80 to I-294 to I-88 and then to I-39.
Its the route we take home any time we go east of the Chicago area. Its quicker, and you only have heavy Chicago traffic from about the 25 mile marker in Indiana to past Aurora, IL on I-88.
An I-pass is $10.00 for a transponder and can be purchased at any oasis on the tollway. You will cut the 5 tolls on the route I gave you in half. If you are from out east and already have an EZ Pass, they work in IL.
I-88 will take you to the Quad Cities (Moline, Rock Island in IL and Davenport and Bettendorf in IA) where you can hook back up with I-80 should you choose to go that way.
If you choose to go I-39/I-90, when you get to the junction of I-90/I-94 in Tomah, WI, stay on I-90 to SD. You will avoid the Minneapolis area which has horrible expressways. Especially I-494 around the north side which is the preferred route. When we came through there in May, eastbound for home, lots of construction.
Have fun on your trip.
Stan