The fair place to meet is Albuquerque, NM — the city closest to the midpoint of Omaha and Tucson. From the farther side that’s about 15 hr 7 min of driving.
Recommended midpoint
Albuquerque, NM
From Omaha
15 hr 7 min
721 mi to Albuquerque
From Tucson
6 hr 40 min
318 mi to Albuquerque
Tucson has the shorter trip; the split is off by about 8 hr 27 min. The alternatives below can even it out. Omaha and Tucson are about 1,038 miles apart.
Omaha and Tucson are about 1,038 miles apart by road. Split the difference and you arrive near Albuquerque, the city closest to the halfway point between them. That puts roughly 15 hr 7 min of driving on the Omaha side and 6 hr 40 min on the Tucson 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. Albuquerque still makes a fair, central place for Omaha and Tucson to converge, splitting the travel instead of asking one side to cross the country.
If Albuquerque doesn't have what you're after, Denver and Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Omaha and Tucson.
Albuquerque is the most populous city in the U.S. state of New Mexico. Founded in 1706 as La Villa de Alburquerque by Santa Fe de Nuevo México governor Francisco Cuervo y Valdés, and named in honor of Francisco Fernández de la Cueva, 10th Duke of Alburquerque… Read more →
Omaha is the most populous city in the U.S. state of Nebraska. It is located in the Midwestern United States along the Missouri River, about 10 mi (15 km) north of the mouth of the Platte River. Read more →
Tucson is the county seat of and the most populated city in Pima County, Arizona, United States. Read more →
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.
Estimates use straight-line distance and typical road speeds; real drive times vary with route and traffic.