NYC is one of a number of world cities known by acronyms or nicknames:

• Rio For Rio de Janeiro
• HK For Hong Kong
• TJ For Tijuana
• KL For Kuala Lumpur
• TO For Toronto
• Joburg For Johannesburg

There's even a whole country that goes by its initials: UK.

So, stop thinking this is some American thing, it's just a way that people shorten the names of common cities that have a few too many syllables to be convenient.