Hello mteh,
Right along I-90 is Missoula, MT, as fun of a college town as there is anywhere. Breakfast at The Oxford, served 24/7, is especially enjoyable when the bars close and the crowd flock to The Oxford.
A little further down the road, at Butte, is the Berkley Pit, one of the largest excavations on the planet, with a nice (and safe) viewing platform. A short distance across town is a very good mining museum.
Lay persons with even casual interest in geology would enjoy "Roadside Geology of Montana" inasmuch as it describes what you're seeing in the form of a road log for the major highways.
Lastly, since you seem to have a bit of time, you could venture south down US 93 from Missoula, through the very scenic Bitterroot Valley, to Lost Trail Pass, and east from there into the Big Hole, which to my experience is the most beautiful alpine valley in the Lower 48. Staying on MT 43 to and through Wisdom brings you to the Big Hole National Battlefield, then Wisdom, Wise River, and Dewey, back to Divide, just a short hop from re-joining I-90 at the western edge of Butte. Turning south at Wisdom on MT 278 takes you through Jackson, MT, where a neat old hot spring resort hotel is, thence to Dillon, where you can jog up on MT 41 to Twin Bridges and on back up to I-90 at Whitehall, or turn south at Twin Bridges through Ennis to West Yellowstone via Quake Lake (there's that geology lesson again). After a drive-through of Yellowstone NP, if the snow hasn't flown a great deal, you could exit out the Lamar Valley to the Northeast entrance via the Beartooth Highway. If the weather's closed the road, go out the East entrance to Cody, WY, past Devil's Tower, see the Black Hills and Badlands, and on across I-90.
Enjoy planning and taking your RoadTrip!
Foy