The fair place to meet is El Paso, TX — the city closest to the midpoint of Houston and Los Angeles. From the farther side that’s about 14 hr 40 min of driving.
Recommended midpoint
El Paso, TX
From Houston
14 hr 8 min
674 mi to El Paso
From Los Angeles
14 hr 40 min
700 mi to El Paso
Houston has the shorter trip; the split is off by about 32 min. The alternatives below can even it out. Houston and Los Angeles are about 1,371 miles apart.
Houston and Los Angeles are about 1,371 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 8 min of driving on the Houston side and 14 hr 40 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. El Paso still makes a fair, central place for Houston and Los Angeles 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 Tucson are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Houston and Los Angeles.
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 →
Houston is the most populous city in the U.S. state of Texas and the Southern United States. It is the fourth-most populous city in the United States, with a population of 2.3 million 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 →
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.