Miami and Tampa are about 206 miles apart by road. Split the difference and you arrive near Orlando, the city closest to the halfway point between them. That puts roughly 4 hr 18 min of driving on the Miami side and 1 hr 56 min on the Tampa side — the fairest single meeting point among the cities near the middle.
At this range, Orlando works for a same-day meetup: close enough from both Miami and Tampa to meet for lunch or an afternoon and still be home by evening.
If Orlando doesn't have what you're after, Atlanta and Birmingham are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Miami and Tampa.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.