Richmond and Salt Lake City are about 1,848 miles apart by road. Split the difference and you arrive near Kansas City, the city closest to the halfway point between them. That splits the trip almost evenly — about 19 hr 35 min from Richmond and 19 hr 21 min from Salt Lake City.
Over this distance most people will fly rather than drive the whole way. Kansas City still makes a fair, central place for Richmond 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 Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Richmond and Salt Lake City.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.