Buffalo and Columbus are about 294 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 38 min of driving on the Buffalo side and 3 hr 9 min on the Columbus 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 Buffalo and Columbus to meet for lunch or an afternoon and still be home by evening.
If Cleveland doesn't have what you're after, Pittsburgh and Detroit are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Buffalo and Columbus.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.