Louisville and Seattle are about 1,939 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That splits the trip almost evenly — about 21 hr 43 min from Louisville and 21 hr 23 min from Seattle.
Over this distance most people will fly rather than drive the whole way. Denver still makes a fair, central place for Louisville and Seattle to converge, splitting the travel instead of asking one side to cross the country.
If Denver doesn't have what you're after, Salt Lake City and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Louisville and Seattle.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.