Detroit and Omaha are about 667 miles apart by road. Split the difference and you arrive near Chicago, the city closest to the halfway point between them. That puts roughly 4 hr 58 min of driving on the Detroit side and 9 hr 3 min on the Omaha side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Chicago suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Chicago doesn't have what you're after, Milwaukee and Indianapolis are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Detroit and Omaha.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.