OK, this gets a little complicated, but it's worth it, OK?
Take the subway up to the George Washington Bridge and get off the train and walk across the bridge on the North side of the bridge's pedestrian walkway, not on the South side.
When you get to the Jersey side of the bridge, look around and you'll find a stairway going up to the start of a great hiking trail that winds all around in Palisades Park, which runs from just south of the bridge all the way up to Alpine, NJ, which is about 9 miles or so.
Now, bear in mind, I am NOT referring to the Henry Hudson Drive, which is the road for cars that runs through that park, no, this is a dirt hiking trail that is up above, on the top of the cliffs.
Like I said, it might be a little hard to find the start of the trail on the Jersey side of the bridge, but, trust me, it's there and it's well worth it! I used to ride my mountain bike up there all the time, and it was really great!!
Good luck!