Times Square became known as the "Cross-Roads of the World" by about 1923-1924. The nickname had been used before for European cities (London, Paris, Rome) or the Near East.

It was soon thereafter that wags called Broadway the "double-cross-roads of the world." Some people look for the worm in every apple.


19 January 1924, New York (NY) Times, pg. 15 ad:
Cross-Roads of the World

The Times Square district of New York City has been called the "cross-roads of the world." More than 52,000 automobiles pass through Times Square every twenty-four hours on business or pleasure.

25 February 1924, New York (NY) Times, pg. 14:
"The cross-roads of the world" looked more like Gopher Prairie's Main Street to-day.

19 March 1926, New York (NY) Herald Tribune, pg. 8 ad:
The Paramount Building
at the
Cross-Roads of the World
Times Square
43rd to 44th Streets

Google Books
Broadway Portraits
By Samuel Marx
New York, NY: Donald Flamm
1929
Pg. 5:
You may have never heard the name of some of them. But they are part, particle and parcel of New York's Main Stem, Hardened Artery, Great White Way, Incandescent Lane, Mazda Boulevard, Chow Mein Stem, Double Cross-Roads of the World, Two-Times Square, or, as somebody once called it, Broadway.