It is New York State or the state of New York.
It's New York State. You will see the word "state" in "New York State" uncapitalized all the time, even in newspapers and magazines, which presumably should know better. But that is wrong. People...
The City of New York IS IN the State of New York. It is is the southern portion of the state.
New York State is 18,998,429 New York City is 8,125,497
Yes, it is.