Miami and New York are about 1,092 miles apart by road. Split the difference and you arrive near Raleigh, the city closest to the halfway point between them. That puts roughly 14 hr 38 min of driving on the Miami side and 8 hr 53 min on the New York 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. Raleigh still makes a fair, central place for Miami and New York to converge, splitting the travel instead of asking one side to cross the country.
If Raleigh doesn't have what you're after, Charlotte and Richmond are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Miami and New York.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.