Cleveland and Miami are about 1,091 miles apart by road. Split the difference and you arrive near Charlotte, the city closest to the halfway point between them. That puts roughly 9 hr 8 min of driving on the Cleveland side and 13 hr 44 min on the Miami side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Charlotte still makes a fair, central place for Cleveland and Miami to converge, splitting the travel instead of asking one side to cross the country.
If Charlotte doesn't have what you're after, Raleigh and Atlanta are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Cleveland and Miami.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.