Denver and New York are about 1,627 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 14 hr 55 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. Chicago still makes a fair, central place for Denver and New York 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 Milwaukee are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Denver and New York.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.