It is estimated that nearly a hundred thousand people live in New York Chinatown which makes it the largest Chinese enclave in New York City. It dates back to the second half of the 19th century and for a long time (almost a century) its population was mostly male.
The Chinese culture is ever present and the festivities (e.g. Chinese New Year) are definitely worth visiting. Also, there is the Museum of Chinese in America which offers information on the development of Chinese culture in the American environment.
If you have a sweet tooth, you might want to visit Aji Ichiban - a Chinese shop with individually sold sweets and various snacks.
In case you prefer a bit of greenery, head to the Columbus Park where there are always some talented street performers (e.g. performing Chinese music).
It is also a good place to go shopping for groceries and food in general because both are quite cheap there. And above all, it is a great spot to taste traditional Chinese cuisine.
Official website http://www.explorechinatown.com/
Coordinates 40°42'59.667" N -73°59'47.412" E