El Paso and Nashville are about 1,167 miles apart by road. Split the difference and you arrive near Dallas, the city closest to the halfway point between them. That puts roughly 11 hr 57 min of driving on the El Paso side and 12 hr 55 min on the Nashville 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 El Paso and Nashville to converge, splitting the travel instead of asking one side to cross the country.
If Dallas doesn't have what you're after, Oklahoma City and Austin are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between El Paso and Nashville.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.