Atlanta and El Paso are about 1,289 miles apart by road. Split the difference and you arrive near Dallas, the city closest to the halfway point between them. That puts roughly 15 hr 5 min of driving on the Atlanta side and 11 hr 57 min on the El Paso 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. Dallas still makes a fair, central place for Atlanta and El Paso to converge, splitting the travel instead of asking one side to cross the country.
If Dallas doesn't have what you're after, Houston and Austin are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Atlanta and El Paso.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.