Oklahoma City and Salt Lake City are about 861 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That puts roughly 10 hr 34 min of driving on the Oklahoma City side and 7 hr 46 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. Denver still makes a fair, central place for Oklahoma City and Salt Lake City to converge, splitting the travel instead of asking one side to cross the country.
If Denver doesn't have what you're after, Albuquerque and El Paso are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Oklahoma City and Salt Lake City.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.