Passports are only needed when you go out of your country. So no you don’t need a passport to go to New York. And you also need a ID or else you need something to prove it

You only need it if you have no other form of government photo ID.
If you use the passport, you will actually travel a bit faster through security as a drivers license is easier to fake than a passport so security takes more time to look over the license to make sure it not a fake.

Here is info on how to apply for a NY State ID if you do not have one or had your license taken away.

No, passports are only needed for international travel. To fly within the U.S. or its territories you just need a gov’t issued photo I.D. like a drivers license or state I.D. card.