New Orleans and Sacramento are about 1,880 miles apart by road. Split the difference and you arrive near Albuquerque, the city closest to the halfway point between them. That puts roughly 21 hr 33 min of driving on the New Orleans side and 17 hr 55 min on the Sacramento 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 New Orleans and Sacramento 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 New Orleans and Sacramento.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.