Omaha and Phoenix are about 1,035 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 12 hr 17 min on the Phoenix 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 Phoenix 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 Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Omaha and Phoenix.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.