The fair place to meet is El Paso, TX — the city closest to the midpoint of Los Angeles and New Orleans. From the farther side that’s about 20 hr 34 min of driving.
Recommended midpoint
El Paso, TX
From Los Angeles
14 hr 40 min
700 mi to El Paso
From New Orleans
20 hr 34 min
981 mi to El Paso
Los Angeles has the shorter trip; the split is off by about 5 hr 54 min. The alternatives below can even it out. Los Angeles and New Orleans are about 1,669 miles apart.
Los Angeles and New Orleans are about 1,669 miles apart by road. Split the difference and you arrive near El Paso, the city closest to the halfway point between them. That puts roughly 14 hr 40 min of driving on the Los Angeles side and 20 hr 34 min on the New Orleans 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. El Paso still makes a fair, central place for Los Angeles and New Orleans to converge, splitting the travel instead of asking one side to cross the country.
If El Paso doesn't have what you're after, Albuquerque and San Antonio are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Los Angeles and New Orleans.
El Paso is a city in and the county seat of El Paso County, Texas, United States. It is the 22nd-most populous city in the U.S., sixth-most populous city in Texas, and the most populous city in West Texas with a population of 678,815 at the 2020 census. 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 →
New Orleans is a consolidated city-parish located along the Mississippi River in the U.S. state of Louisiana. 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.