Miami and Salt Lake City are about 2,088 miles apart by road. Split the difference and you arrive near Dallas, the city closest to the halfway point between them. That puts roughly 23 hr 17 min of driving on the Miami side and 20 hr 57 min on the Salt Lake City 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. Dallas still makes a fair, central place for Miami and Salt Lake City to converge, splitting the travel instead of asking one side to cross the country.
If Dallas doesn't have what you're after, Oklahoma City and Austin are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Miami and Salt Lake City.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.