The fair place to meet is Albuquerque, NM — the city closest to the midpoint of Kansas City and Los Angeles. 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 Los Angeles
13 hr 54 min
663 mi to Albuquerque
Los Angeles has the shorter trip; the split is off by about 1 hr 12 min. The alternatives below can even it out. Kansas City and Los Angeles are about 1,354 miles apart.
Kansas City and Los Angeles are about 1,354 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 13 hr 54 min on the Los Angeles 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 Los Angeles 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 El Paso are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Kansas City and Los Angeles.
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 →
Los Angeles (LA) is the most populous city in the U.S. state of California, and the commercial, financial, and cultural center of Southern California. 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.