Birmingham and Boise are about 1,723 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That puts roughly 22 hr 55 min of driving on the Birmingham side and 13 hr 21 min on the Boise 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 Birmingham and Boise to converge, splitting the travel instead of asking one side to cross the country.
If Denver doesn't have what you're after, Oklahoma City and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Birmingham and Boise.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.