Birmingham and Hartford are about 959 miles apart by road. Split the difference and you arrive near Richmond, the city closest to the halfway point between them. That puts roughly 12 hr 29 min of driving on the Birmingham side and 8 hr 6 min on the Hartford 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. Richmond still makes a fair, central place for Birmingham and Hartford to converge, splitting the travel instead of asking one side to cross the country.
If Richmond doesn't have what you're after, Raleigh and Washington are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Birmingham and Hartford.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.