A lovely loop in Bear Mountain State Park that makes for a great weekend afternoon hike.
To get to Bear Mountain State Park from NYC with mass transport, you can take the Short Line bus right to the trailhead. The bus runs on weekends and takes a while but is worth it if you are car-less. The bus drops you off in front of a lodge and a huge grass lawn. From here, head south to the far parking area and look for the trail through a tunnel under a road.
Basically, follow the Blue, Cornell Mine Trail
south. You'll have to hike along the road for a very short distance and then duck back into the woods near a waterfall. Keep going south to a red-blazed, Ramapo-Dunderberg Trail
to your left (east). The trail will bring you out towards the Hudson River and some good views. Head back east to rejoin the Blue, Timp-Torne Trail
You'll do some seemingly unnecessary elevation gain and loss before meeting up with yet another red-blazed trail, 1777 Trail
. Head north, and avoid turning off on one of the many unmarked forest roads. Finally, look for the Yellow, Suffern-Bear Mountain Trail
and head right (northeast). This trail should lead you back to the lodge. The lodge servers beer on the second floor if you have some time to kill before the bus returns.