Columbus and Detroit are about 164 miles apart by road. Split the difference and you arrive near Cleveland, the city closest to the halfway point between them. That puts roughly 3 hr 9 min of driving on the Columbus side and 2 hr 15 min on the Detroit side — the fairest single meeting point among the cities near the middle.
At this range, Cleveland works for a same-day meetup: close enough from both Columbus and Detroit to meet for lunch or an afternoon and still be home by evening.
If Cleveland doesn't have what you're after, Cincinnati and Pittsburgh are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Columbus and Detroit.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.