Times Square was a location in New York City.
History
Times Square was established at some point in the 20th century. (TV: Nikola Tesla's Night of Terror)
In October 1969, an advertisement for International Electromatics was seen there. (PROSE: Times Squared)
On 31 December 1999, millennium celebrations took place in Times Square. (PROSE: The Novel of the Film)
In the 21st century, Times Square was evacuated as the city was overrun by dinosaurs from the Jurassic that appeared when Professor Saurian tried to change Earth history using a "roll-back machine". The Eleventh Doctor defeated Saurian by resetting his machine via "reversing the polarity of the neutron flow". Saurian was taken along with his machine and the dinosaurs back to the Jurassic Age. (COMIC: Dinosaurs in New York!)
A New Times Square existed in New New York. (TV: Gridlock)
Other realities
It was in Times Square in the 2460 New York of one of the realities within the 10,000 Dawns that Graelyn Scythes and Archimedes Von Ahnerabe confronted Artillo Brinzo. They were surprised to see it empty on Christmas Eve except for themselves and their quarry, an early step in their gradual realisation that nearly the entire population of the 10,000 Dawns had been abducted out of time and space by the painted warriors. (PROSE: White Canvas)
Other references
Ryan Sinclair, a native of 2020 Sheffield, professed to the Thirteenth Doctor that he had always wanted to visit Times Square as they visited New York City in the early 1900s, only to learn that Times Square did not yet exist at this point. (TV: Nikola Tesla's Night of Terror)