The fair place to meet is San Antonio, TX — the city closest to the midpoint of El Paso and Houston. From the farther side that’s about 10 hr 31 min of driving.
Recommended midpoint
San Antonio, TX
From El Paso
10 hr 31 min
502 mi to San Antonio
From Houston
3 hr 58 min
189 mi to San Antonio
Houston has the shorter trip; the split is off by about 6 hr 33 min. The alternatives below can even it out. El Paso and Houston are about 674 miles apart.
El Paso and Houston are about 674 miles apart by road. Split the difference and you arrive near San Antonio, the city closest to the halfway point between them. That puts roughly 10 hr 31 min of driving on the El Paso side and 3 hr 58 min on the Houston side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so San Antonio suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If San Antonio doesn't have what you're after, Austin and Dallas are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between El Paso and Houston.
San Antonio is a city in the U.S. state of Texas. It is the seventh-most populous city in the United States, the second-most populous city in Texas, and the second-most populous city in the Southern U.S., with a population of 1.43 million at the 2020 census. Read more →
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 →
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.