When new york city is in a sentence would you capitalize all three words?

You would only capitalize "New York City" when it is used as a proper noun, meaning it's the name of a specific place. Here's how it works:

* "New York City is a bustling metropolis." (Correct)

* "The mayor of new york city announced a new policy." (Incorrect, "New York City" should be capitalized)

Let me know if you have any other questions!