@Roberta,
My family used to take weekend excursions to Bear Mountain and Harriman Park. There used to be lots of picnic areas where you could cook over a grill; it was pretty cool. Before the Palisades Parkway was built, we'd drive up Route 9W and get to observe the
Mothball Fleet.
If I recall, "Bear" Mountain got its name because of it resembled the silhouette of a sleeping bear.