Las Vegas and New York are about 2,228 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 22 hr 56 min on the New York 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 New York to converge, splitting the travel instead of asking one side to cross the country.
If Kansas City doesn't have what you're after, Omaha and Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Las Vegas and New York.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.