The fair place to meet is Kansas City, MO — the city closest to the midpoint of New York and Salt Lake City. From the farther side that’s about 22 hr 56 min of driving.
Recommended midpoint
Kansas City, MO
From New York
22 hr 56 min
1,094 mi to Kansas City
From Salt Lake City
19 hr 21 min
923 mi to Kansas City
Salt Lake City has the shorter trip; the split is off by about 3 hr 35 min. The alternatives below can even it out. New York and Salt Lake City are about 1,968 miles apart.
New York and Salt Lake City are about 1,968 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 22 hr 56 min of driving on the New York side and 19 hr 21 min on the Salt Lake City 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 New York and Salt Lake City 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 Chicago are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between New York and Salt Lake City.
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 →
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 →
Salt Lake City, often shortened to Salt Lake or SLC, is the capital and most populous city of the U.S. state of Utah. It is the county seat of Salt Lake County, the most populous county in the state. 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.