Las Vegas and Philadelphia are about 2,172 miles apart by road. Split the difference and you arrive near Kansas City, the city closest to the halfway point between them. That puts roughly 23 hr 55 min of driving on the Las Vegas side and 21 hr 41 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. Kansas City still makes a fair, central place for Las Vegas and Philadelphia to converge, splitting the travel instead of asking one side to cross the country.
If Kansas City doesn't have what you're after, Oklahoma City and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Las Vegas and Philadelphia.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.