My NY return status says ready to mail. My printed return(from TurboTax) says NY state requires e-file. These 2 seem to be contradicting.

They are contradicting, however, what happening is that New York state really encourages e-filing.  But that being said, there are still many people who need to file by mail.  You can find the New York mailing address here:  https://www.tax.ny.gov/pit/file/return_assembly_mail.htm.