Hartford and Memphis are about 1,043 miles apart by road. Split the difference and you arrive near Columbus, the city closest to the halfway point between them. That puts roughly 11 hr 36 min of driving on the Hartford side and 10 hr 41 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. Columbus still makes a fair, central place for Hartford and Memphis to converge, splitting the travel instead of asking one side to cross the country.
If Columbus doesn't have what you're after, Pittsburgh and Cincinnati are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Hartford and Memphis.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.