Omaha and Salt Lake City are about 831 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 13 min of driving on the Omaha 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 Omaha 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 Kansas City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Omaha and Salt Lake City.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.