Is the expression offensive or illegal?

New York is a state not a nation. The United States of America is a nation. It is composed of 50 states and New York is one of them.

The United States is a nation of immigrants i.e. of different nationalities or ethnic groups.

As stated previously Newyork is a state. If you are refering to the city it would be preferable to use the term "New Yoks City"
A statement such as "New York city was built by people of differnet cultures" would not be offensive.

Wouldn't a bit of attention to spelling be helpful to a person learning English?

Thank you all.