Boise and Memphis are about 1,506 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That puts roughly 13 hr 21 min of driving on the Boise side and 18 hr 24 min on the Memphis 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. Denver still makes a fair, central place for Boise and Memphis to converge, splitting the travel instead of asking one side to cross the country.
If Denver doesn't have what you're after, Albuquerque and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Boise and Memphis.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.