Gouverneur, NY 13642. Telephone: (315) 287-4440. Fax: (315) 287-1858. Click here for directions to our Health Center location in Gouverneur. Business Hours in Gouverneur: Monday & Friday: 7 am to 5; Tuesday - Thursday 7am-7 pm. IF YOU HAVE A MEDICAL EMERGENCY OUTSIDE OF OUR NORMAL BUSINESS HOURS, PLEASE CALL 911..