The fair place to meet is Dallas-Fort Worth, TX — the city closest to the midpoint of Austin and Memphis. From the farther side that’s about 8 hr 48 min of driving.
Recommended midpoint
Dallas-Fort Worth, TX
From Austin
3 hr 49 min
182 mi to Dallas
From Memphis
8 hr 48 min
420 mi to Dallas
Austin has the shorter trip; the split is off by about 4 hr 59 min. The alternatives below can even it out. Austin and Memphis are about 560 miles apart.
Austin and Memphis are about 560 miles apart by road. Split the difference and you arrive near Dallas, the city closest to the halfway point between them. That puts roughly 3 hr 49 min of driving on the Austin side and 8 hr 48 min on the Memphis side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Dallas suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Dallas doesn't have what you're after, Houston and Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Austin and Memphis.
Dallas is a city in the U.S. state of Texas. Located in the state's northern region, it is the ninth-most populous city in the United States and third-most populous city in Texas, with a population of 1.3 million 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 →
Memphis is a city in Shelby County, Tennessee, United States, and its county seat. 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.