Here is the address to send your Federal Amended 1040x
Department of the Treasury
Internal Revenue Service
Kansas City, MO 64999
Here are the mailing addresses for mailing in your New York State Form IT-201-X, Amended Resident Income Tax Return:
If enclosing a payment (check or money order):
STATE PROCESSING CENTER
PO BOX 15555
ALBANY NY 12212-5555
If not enclosing a payment:
STATE PROCESSING CENTER
PO BOX 61000
ALBANY NY 12261-0001
Instructions to Form IT-201-X:
https://www.tax.ny.gov/pdf/current_forms/it/it201xi.pdf