Las Vegas and Omaha are about 1,091 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That puts roughly 12 hr 41 min of driving on the Las Vegas side and 10 hr 13 min on the Omaha 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 Las Vegas and Omaha 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 Salt Lake City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Las Vegas and Omaha.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.