Here's a great loop out of the parking lot at Bear Mtn.:<br><br>
Hit the Suffern-Bear Mtn. trail (yellow blaze) above the skate rink; take the SBM until it connects with the Ramapo-Dunderberg (red blaze); take the RD until it connects with the Appalachian Trail (white blaze); the AT will lead you back to parking lot. There's a lot of climbing in this loop--SMB takes you over West Mountain, the AT will take you back over it further north and then Bear Mtn. But beyond those climbs, there are lots of steep ups and downs.<br><br>
I'm partial these days to heading a bit farther north, to Cold Spring on the other side of the Hudson. The climbs are generally bigger, and a few of the trails are less rocky.<br><br>
BTW, you can probably pick up maps at Tent and Trail in Tribeca. Once you have those, there are a lot of nice trails south of West Mountain.