What do I do if someone in NY is trying to use my Apple ID.

If this is an e-mail you received, or a popup on the screen,  about the time you were actually logging in, there is probably nothing to worry about. The location in the e-mail is where your ISP reported it. If their servers are in a location distant from you, there will be a large error.

If you weren't trying to sign in, you might want to consider changing your password and making sure it is a strong one. You can also add 2 Factor Authentication to your account for more security. If the attempts continue, you might want to consider a name change.

Apple ID has been compromised

 Apple ID Password Change

Note the restrictions in the article.

Apple ID Name Change

 What to do after you change your Apple ID or password - Apple Support     I suggest doing this before you change your Apple ID or password.

 Apple ID -Two-factor authentication

 Two Factor Authentification availability

 Apple ID - Using app-specific passwords

Apple ID - Two Step Verification App Specific Passwords

Apple ID - Two Step Verifications FAQ