Minneapolis and Tucson are about 1,295 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That puts roughly 14 hr 39 min of driving on the Minneapolis side and 12 hr 57 min on the Tucson side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Denver still makes a fair, central place for Minneapolis and Tucson to converge, splitting the travel instead of asking one side to cross the country.
If Denver doesn't have what you're after, Oklahoma City and Albuquerque are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Minneapolis and Tucson.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.