Philadelphia and Salt Lake City are about 1,920 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 21 hr 41 min of driving on the Philadelphia side and 19 hr 21 min on the Salt Lake City 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 Philadelphia and Salt Lake City 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 Minneapolis are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Philadelphia and Salt Lake City.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.