Dallas and Las Vegas are about 1,069 miles apart by road. Split the difference and you arrive near Albuquerque, the city closest to the halfway point between them. That puts roughly 12 hr 18 min of driving on the Dallas side and 10 hr 7 min on the Las Vegas 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. Albuquerque still makes a fair, central place for Dallas and Las Vegas to converge, splitting the travel instead of asking one side to cross the country.
If Albuquerque doesn't have what you're after, El Paso and Tucson are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Dallas and Las Vegas.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.