According to the USGS GNIS (http://www.geonames.usgs.gov), the state of New York in the United States has 11 peaks named Bear Mountain. The most widely known is the one in Orange County, just north of the New York metropolitan area and of which the name for Bear Mountain State Park is derived.
Web Sites and Links
Bear Mountain State ParkOffers play field, picnic area, dock, fishing access, swimming, ice skating, hiking, biking and cross-country skiing.
Blauvelt State ParkForested area in Rockland County with hiking trails, no set hours. Includes directions.