Austin and Phoenix are about 868 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 7 hr 15 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. El Paso still makes a fair, central place for Austin and Phoenix 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 Phoenix.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.