The fair place to meet is Kansas City, MO — the city closest to the midpoint of Boston and Los Angeles. From the farther side that’s about 28 hr 24 min of driving.
Recommended midpoint
Kansas City, MO
From Boston
26 hr 10 min
1,248 mi to Kansas City
From Los Angeles
28 hr 24 min
1,354 mi to Kansas City
Boston has the shorter trip; the split is off by about 2 hr 14 min. The alternatives below can even it out. Boston and Los Angeles are about 2,591 miles apart.
Boston and Los Angeles are about 2,591 miles apart by road. Split the difference and you arrive near Kansas City, the city closest to the halfway point between them. That puts roughly 26 hr 10 min of driving on the Boston side and 28 hr 24 min on the Los Angeles 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. Kansas City still makes a fair, central place for Boston and Los Angeles to converge, splitting the travel instead of asking one side to cross the country.
If Kansas City doesn't have what you're after, Omaha and Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Boston and Los Angeles.
Kansas City, abbreviated KC or KCMO, is the largest city in the U.S. state of Missouri by both population and area. It is located on the Missouri River at its confluence with the Kansas River, within Jackson, Clay, Platte and Cass counties. Read more →
Boston is the capital and most populous city of the U.S. state of Massachusetts. It serves as a cultural and financial center of New England, a region of the Northeastern United States. Read more →
Los Angeles (LA) is the most populous city in the U.S. state of California, and the commercial, financial, and cultural center of Southern California. Read more →
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.
Estimates use straight-line distance and typical road speeds; real drive times vary with route and traffic.