High Quality Content by WIKIPEDIA articles! New York State Route 403 (NY 403) is a short state highway located entirely within Putnam County. It connects NY 9D in Philipstown at its northern/western end to US 9 in Graymoor, where the Appalachian Trail crosses both highways. At that intersection, NY 403 is signed as a route to the Bear Mountain Bridge, although it is a rather circuitous route there.