The fair place to meet is Kansas City, MO — the city closest to the midpoint of Los Angeles and New York. From the farther side that’s about 28 hr 24 min of driving.
Recommended midpoint
Kansas City, MO
From Los Angeles
28 hr 24 min
1,354 mi to Kansas City
From New York
22 hr 56 min
1,094 mi to Kansas City
New York has the shorter trip; the split is off by about 5 hr 28 min. The alternatives below can even it out. Los Angeles and New York are about 2,446 miles apart.
Los Angeles and New York are about 2,446 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 28 hr 24 min of driving on the Los Angeles side and 22 hr 56 min on the New York 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 Los Angeles and New York to converge, splitting the travel instead of asking one side to cross the country.
If Kansas City 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 Los Angeles and New York.
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 →
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 →
New York, often called New York City (NYC), is the most populous city in the United States. It is located at the southern tip of New York State on New York Harbor, one of the world's largest natural harbors. 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.