The fair place to meet is El Paso, TX — the city closest to the midpoint of Houston and Tucson. 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 Tucson
5 hr 33 min
265 mi to El Paso
Tucson has the shorter trip; the split is off by about 8 hr 35 min. The alternatives below can even it out. Houston and Tucson are about 939 miles apart.
Houston and Tucson are about 939 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 5 hr 33 min on the Tucson 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 Tucson to converge, splitting the travel instead of asking one side to cross the country.
If El Paso doesn't have what you're after, San Antonio and Austin are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Houston and Tucson.
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 →
Tucson is the county seat of and the most populated city in Pima County, Arizona, United States. 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.