The fair place to meet is El Paso, TX — the city closest to the midpoint of Houston and Phoenix. 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 Phoenix
7 hr 15 min
345 mi to El Paso
Phoenix has the shorter trip; the split is off by about 6 hr 53 min. The alternatives below can even it out. Houston and Phoenix are about 1,014 miles apart.
Houston and Phoenix are about 1,014 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 7 hr 15 min on the Phoenix 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 Phoenix 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 Houston and Phoenix.
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 →
Phoenix is the capital and most populous city of the U.S. state of Arizona. With over 1.6 million residents at the 2020 census, Phoenix is the fifth-most populous city in the United States and the most populous state capital. 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.