When you tell the program that you wish to mail your return, an instruction page with an address should be printed for you.  But, here is the mailing address information from the NY website.

You must include the following on your envelope:

• your return address
• enough postage (some returns require additional postage)

If you are NOT including a payment, mail your return to:

STATE PROCESSING CENTER
PO BOX 61000
ALBANY NY 12261-0001

If you ARE including a payment (check or money order), mail your return (including Form IT-201-V) to:

STATE PROCESSING CENTER
PO BOX 15555
ALBANY NY 12212-5555
 

You may send your income tax return and tax payment using a private delivery service instead of the U.S. Postal Service. If you use any private delivery service, send the forms to:

NYS TAX DEPARTMENT
RPC - PIT
90 COHOES AVE
GREEN ISLAND NY 12183-1515

https://www.tax.ny.gov/pit/file/return_assembly_mail.htm