Las Vegas and Orlando are about 2,029 miles apart by road. Split the difference and you arrive near Dallas, the city closest to the halfway point between them. That puts roughly 22 hr 25 min of driving on the Las Vegas side and 20 hr 9 min on the Orlando 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. Dallas still makes a fair, central place for Las Vegas and Orlando to converge, splitting the travel instead of asking one side to cross the country.
If Dallas doesn't have what you're after, Austin and San Antonio are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Las Vegas and Orlando.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.