Do you need to bring your ID card to New York?

To travel to New York, you must bring your passport. However, your ID card can also be useful to have with you.

An ID card is not enough to travel to New York

To enter the United States, you must have a valid passport. An ID card alone will not get you through US immigration, so it’s not useful for entry requirements to the United States.
When you apply for ESTA travel authorization, US immigration will ask for your passport number, not your ID card number.
That said, there are 3 situations where bringing your ID card to New York (or driver’s license if you’re from Canada) can be useful.

To prove your age without showing your passport. If you’re just over 21, bars and tobacco shops may ask for ID if they think you look too young. Your ID card works perfectly for this—there’s no need to show your passport. It’s better not to carry your passport around all day; you risk losing it. Leave it in your hotel room’s safe instead.
To claim a senior discount. Your ID card is also sufficient to prove your age if you qualify for a reduced admission price at an attraction.
As a deposit for audioguides. Museums often ask you to leave an ID as a deposit when you borrow an audioguide. Use your ID card instead of your passport—if there’s any mix-up, you don’t want your passport handed to someone else by mistake.