Cleveland and Detroit are about 90 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 26 min from Detroit.
At this range, Columbus works for a same-day meetup: close enough from both Cleveland and Detroit to meet for lunch or an afternoon and still be home by evening.
If Columbus doesn't have what you're after, Pittsburgh and Buffalo are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Cleveland and Detroit.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.