The fair place to meet is Albuquerque, NM — the city closest to the midpoint of Los Angeles and Memphis. From the farther side that’s about 19 hr 39 min of driving.
Recommended midpoint
Albuquerque, NM
From Los Angeles
13 hr 54 min
663 mi to Albuquerque
From Memphis
19 hr 39 min
937 mi to Albuquerque
Los Angeles has the shorter trip; the split is off by about 5 hr 45 min. The alternatives below can even it out. Los Angeles and Memphis are about 1,600 miles apart.
Los Angeles and Memphis are about 1,600 miles apart by road. Split the difference and you arrive near Albuquerque, the city closest to the halfway point between them. That puts roughly 13 hr 54 min of driving on the Los Angeles side and 19 hr 39 min on the Memphis 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 Los Angeles and Memphis to converge, splitting the travel instead of asking one side to cross the country.
If Albuquerque doesn't have what you're after, El Paso and Denver are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Los Angeles and Memphis.
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 →
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 →
Memphis is a city in Shelby County, Tennessee, United States, and its county seat. 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.