New York is the name of both a city and a US state based on the east coast. The term "New York City" is used to distinguish the city from the state, which is officially called the State of New York.
Anderson universeIn the Anderson universe, the state was hit by the Global T-Virus pandemic. Most, if not all, of its population was killed off or infected over the course of five years after the Raccoon City Incident in 2002 and proceeding the events in the city of Las Vegas in Nevada. A replicated portion of New York City was used by Umbrella as a component of the Umbrella Prime facility to serve as a simulation for controlled biohazardous outbreaks in urban environments. Given that the simulated outbreaks in New York involved the huge and hideous Axemen, it is possible that they were involved in the real thing.
After unleashing the anti-virus that will ultimately bring an end to the Global T-Virus pandemic, Alice makes her way through the ruins of New York on an Umbrella motorcycle where she is chased by three flying mutations.
In the Perry universe, New York was the home state of George Trevor and his family, which was about an hours drive from Raccoon City, Pennsylvania.