The fair place to meet is El Paso, TX — the city closest to the midpoint of Austin and Las Vegas. From the farther side that’s about 12 hr 12 min of driving.
Recommended midpoint
El Paso, TX
From Austin
11 hr 4 min
528 mi to El Paso
From Las Vegas
12 hr 12 min
582 mi to El Paso
Austin has the shorter trip; the split is off by about 1 hr 8 min. The alternatives below can even it out. Austin and Las Vegas are about 1,083 miles apart.
Austin and Las Vegas are about 1,083 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 11 hr 4 min of driving on the Austin 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 Austin 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 Austin 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 →
Austin is the capital city of the U.S. state of Texas. With a population of 961,855 at the 2020 census, it is the 12th-most populous city in the U.S., fifth-most populous city in Texas, and second-most populous U.S. 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.