Cleveland and Pittsburgh are about 115 miles apart by road. Split the difference and you arrive near Columbus, the city closest to the halfway point between them. That splits the trip almost evenly — about 3 hr 9 min from Cleveland and 3 hr 24 min from Pittsburgh.
At this range, Columbus works for a same-day meetup: close enough from both Cleveland and Pittsburgh to meet for lunch or an afternoon and still be home by evening.
If Columbus doesn't have what you're after, Detroit and Buffalo are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Cleveland and Pittsburgh.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.