The fair place to meet is Albuquerque, NM — the city closest to the midpoint of Los Angeles and Nashville. From the farther side that’s about 23 hr 25 min of driving.
Recommended midpoint
Albuquerque, NM
From Los Angeles
13 hr 54 min
663 mi to Albuquerque
From Nashville
23 hr 25 min
1,116 mi to Albuquerque
Los Angeles has the shorter trip; the split is off by about 9 hr 31 min. The alternatives below can even it out. Los Angeles and Nashville are about 1,777 miles apart.
Los Angeles and Nashville are about 1,777 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 23 hr 25 min on the Nashville 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 Nashville 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 El Paso are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Los Angeles and Nashville.
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 →
Nashville is the capital and most populous city in the U.S. state of Tennessee. It is the seat of Davidson County in Middle Tennessee, located on the Cumberland River. 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.