Multiple realities(covers information from several alternate timelines)
Times Square was a famous square, located on Upper Broadway, in New York City on Earth.
In The Big Good-Bye, on one New Year's Day, Barney Kollecher, a police officer, had his fellow officers posted at this location. They were to keep the peace, and to arrest petty criminals and bullies. (TNG: "The Big Goodbye")
The pages seen in the episode were actually from the detective novel,
The Listening Man, by author John A. Moroso. This novel was published in 1924. Information on Times Square was from page 178.
In an alternate timeline, Adolf Hitler received a hero's welcome in Times Square when he toured the conquered city in 1944. (ENT: "Storm Front, Part II")