The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of Austin and Denver. From the farther side that’s about 10 hr 34 min of driving.
Recommended midpoint
Oklahoma City, OK
From Austin
7 hr 32 min
360 mi to Oklahoma City
From Denver
10 hr 34 min
504 mi to Oklahoma City
Austin has the shorter trip; the split is off by about 3 hr 2 min. The alternatives below can even it out. Austin and Denver are about 772 miles apart.
Austin and Denver are about 772 miles apart by road. Split the difference and you arrive near Oklahoma City, the city closest to the halfway point between them. That puts roughly 7 hr 32 min of driving on the Austin side and 10 hr 34 min on the Denver side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Oklahoma City suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Oklahoma City doesn't have what you're after, Albuquerque and Dallas are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Austin and Denver.
Oklahoma City, often shortened to OKC, is the capital and most populous city in the U.S. state of Oklahoma. It is the 21st-most populous U.S. city and 8th largest in the Southern United States, with a population of 681,054 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 →
Denver is the capital and most populous city of the U.S. state of Colorado. Officially a consolidated city and county, it is located in the South Platte River valley on the western edge of the High Plains, and is just east of the Front Range of the Rocky… 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.