The fair place to meet is El Paso, TX — the city closest to the midpoint of Houston and Las Vegas. From the farther side that’s about 14 hr 8 min of driving.
Recommended midpoint
El Paso, TX
From Houston
14 hr 8 min
674 mi to El Paso
From Las Vegas
12 hr 12 min
582 mi to El Paso
Las Vegas has the shorter trip; the split is off by about 1 hr 56 min. The alternatives below can even it out. Houston and Las Vegas are about 1,226 miles apart.
Houston and Las Vegas are about 1,226 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 12 hr 12 min on the Las Vegas 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 Las Vegas 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 Las Vegas.
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 →
Las Vegas, colloquially shortened to Vegas, is the most populous city in the U.S. state of Nevada and the county seat of Clark County. It is the 24th-most populous city in the United States, with 641,903 residents at the 2020 census. 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.