The fair place to meet is Albuquerque, NM — the city closest to the midpoint of Houston and Salt Lake City. From the farther side that’s about 15 hr 47 min of driving.
Recommended midpoint
Albuquerque, NM
From Houston
15 hr 47 min
753 mi to Albuquerque
From Salt Lake City
10 hr 10 min
485 mi to Albuquerque
Salt Lake City has the shorter trip; the split is off by about 5 hr 37 min. The alternatives below can even it out. Houston and Salt Lake City are about 1,199 miles apart.
Houston and Salt Lake City are about 1,199 miles apart by road. Split the difference and you arrive near Albuquerque, the city closest to the halfway point between them. That puts roughly 15 hr 47 min of driving on the Houston side and 10 hr 10 min on the Salt Lake City 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. Albuquerque still makes a fair, central place for Houston and Salt Lake City to converge, splitting the travel instead of asking one side to cross the country.
If Albuquerque doesn't have what you're after, El Paso and Denver are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Houston and Salt Lake City.
Albuquerque is the most populous city in the U.S. state of New Mexico. Founded in 1706 as La Villa de Alburquerque by Santa Fe de Nuevo México governor Francisco Cuervo y Valdés, and named in honor of Francisco Fernández de la Cueva, 10th Duke of Alburquerque… 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 →
Salt Lake City, often shortened to Salt Lake or SLC, is the capital and most populous city of the U.S. state of Utah. It is the county seat of Salt Lake County, the most populous county in the state. 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.