New Orleans and Philadelphia are about 1,088 miles apart by road. Split the difference and you arrive near Charlotte, the city closest to the halfway point between them. That puts roughly 13 hr 36 min of driving on the New Orleans side and 9 hr 27 min on the Philadelphia 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. Charlotte still makes a fair, central place for New Orleans and Philadelphia to converge, splitting the travel instead of asking one side to cross the country.
If Charlotte doesn't have what you're after, Atlanta and Raleigh are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between New Orleans and Philadelphia.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.