The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of Nashville and Phoenix. From the farther side that’s about 17 hr 37 min of driving.
Recommended midpoint
Oklahoma City, OK
From Nashville
12 hr 39 min
603 mi to Oklahoma City
From Phoenix
17 hr 37 min
840 mi to Oklahoma City
Nashville has the shorter trip; the split is off by about 4 hr 58 min. The alternatives below can even it out. Nashville and Phoenix are about 1,443 miles apart.
Nashville and Phoenix are about 1,443 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 12 hr 39 min of driving on the Nashville side and 17 hr 37 min on the Phoenix 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. Oklahoma City still makes a fair, central place for Nashville and Phoenix to converge, splitting the travel instead of asking one side to cross the country.
If Oklahoma City doesn't have what you're after, Dallas and Austin are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Nashville and Phoenix.
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 →
Nashville is the capital and most populous city in the U.S. state of Tennessee. It is the seat of Davidson County in Middle Tennessee, located on the Cumberland River. Read more →
Phoenix is the capital and most populous city of the U.S. state of Arizona. With over 1.6 million residents at the 2020 census, Phoenix is the fifth-most populous city in the United States and the most populous state capital. 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.