Translation:Our home is in New York.
Well maybe just your generation. I was born and raised in New York 50 miles west of NYC, from there, we called it 'The City', if you are in New York (the state) at the time many people will say Manhattan, referring to the name of the island. It is much like San Francisco, many natives will correct you if you say 'Frisco': they will say, "It's San Francisco, thank you. Also, NYC is fine in messaging, but for use in proper speech, it comes off as if you might have meant to refer to a university -IMHO, New York City is more clear and proper and the natives will appreciate your kind effort and attention. OMT: In Spanish Nueva York is always understood as the city, and in most parts of the US unless you specifically refer to the State of New York; so New York is usually well understood outside of the state. Sorry if I obsessed, I come from there (it hits home). Thank you for you indulgence. Many cities are fussy this way, however.