Minneapolis and Omaha are about 290 miles apart by road. Split the difference and you arrive near Kansas City, the city closest to the halfway point between them. That puts roughly 8 hr 38 min of driving on the Minneapolis side and 3 hr 28 min on the Omaha side — the fairest single meeting point among the cities near the middle.
At this range, Kansas City works for a same-day meetup: close enough from both Minneapolis and Omaha to meet for lunch or an afternoon and still be home by evening.
If Kansas City doesn't have what you're after, Milwaukee and Chicago are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Minneapolis and Omaha.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.