@jsgmom Check out Breakneck Ridge located near Cold Spring, NY. Along the Hudson. You can actually take Metro North from Grand Central and walk about ten minutes from the train to the trailhead.
Speaking of Metro North you can also take it to Appalachian Trail Station, (on Saturdays and Sundays) and get right on the AT.
One more, Fahnstock State Park, about 75 minutes north of Manhattan, off the Taconic State Parkway. Great hiking, and the AT passes through there also.