Detroit and Kansas City are about 643 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 8 hr 39 min on the Kansas City 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, Indianapolis and Milwaukee are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Detroit and Kansas City.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.