Cleveland and Columbus are about 126 miles apart by road. Split the difference and you arrive near Detroit, the city closest to the halfway point between them. That puts roughly 2 hr 15 min of driving on the Cleveland side and 3 hr 26 min on the Columbus side — the fairest single meeting point among the cities near the middle.
At this range, Detroit works for a same-day meetup: close enough from both Cleveland and Columbus to meet for lunch or an afternoon and still be home by evening.
If Detroit doesn't have what you're after, Pittsburgh and Cincinnati are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Cleveland and Columbus.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.