The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of Buffalo and Los Angeles. From the farther side that’s about 24 hr 43 min of driving.
Recommended midpoint
Oklahoma City, OK
From Buffalo
23 hr 27 min
1,119 mi to Oklahoma City
From Los Angeles
24 hr 43 min
1,178 mi to Oklahoma City
Buffalo has the shorter trip; the split is off by about 1 hr 16 min. The alternatives below can even it out. Buffalo and Los Angeles are about 2,193 miles apart.
Buffalo and Los Angeles are about 2,193 miles apart by road. Split the difference and you arrive near Oklahoma City, the city closest to the halfway point between them. That puts roughly 23 hr 27 min of driving on the Buffalo side and 24 hr 43 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. Oklahoma City still makes a fair, central place for Buffalo and Los Angeles to converge, splitting the travel instead of asking one side to cross the country.
If Oklahoma City doesn't have what you're after, Kansas City and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Buffalo and Los Angeles.
Oklahoma City, often shortened to OKC, is the capital and most populous city in the U.S. state of Oklahoma. It is the 21st-most populous U.S. city and 8th largest in the Southern United States, with a population of 681,054 at the 2020 census. Read more →
Buffalo is a city in the U.S. state of New York. It lies in Western New York on the eastern shore of Lake Erie and at the head of the Niagara River on the Canada–United States border. 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.