For federal tax returns, the mailing address depends on your state and whether you're including a payment. You can find the specific address for your situation on the IRS website
For New York State tax returns: Addresses for mailing can be found on NYS Department of Taxation and Finance website
For Reference:
Mailing information in TurboTax: The first page in your printout is your instructions. This page gives you the address to send your return to, and any forms you need to include with your return. The instructions to print and mail are at this link.