Denver and Philadelphia are about 1,575 miles apart by road. Split the difference and you arrive near Chicago, the city closest to the halfway point between them. That puts roughly 19 hr 15 min of driving on the Denver side and 13 hr 55 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. Chicago still makes a fair, central place for Denver and Philadelphia to converge, splitting the travel instead of asking one side to cross the country.
If Chicago doesn't have what you're after, Indianapolis and Kansas City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Denver and Philadelphia.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.