The fair place to meet is Albuquerque, NM — the city closest to the midpoint of Kansas City and Tucson. From the farther side that’s about 15 hr 6 min of driving.
Recommended midpoint
Albuquerque, NM
From Kansas City
15 hr 6 min
720 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 26 min. The alternatives below can even it out. Kansas City and Tucson are about 1,034 miles apart.
Kansas City and Tucson are about 1,034 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 6 min of driving on the Kansas City 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 Kansas City 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, Oklahoma City and Denver are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Kansas City 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 →
Kansas City, abbreviated KC or KCMO, is the largest city in the U.S. state of Missouri by both population and area. It is located on the Missouri River at its confluence with the Kansas River, within Jackson, Clay, Platte and Cass counties. 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.