If you don't mind long stretches of highway travel, Palisades Park is one of the most unitentionallly beautiful places to hike in the entire east coast. Long stretches of ugly hiking just parallel to the Palisades Park Interstate Parkway mark the trail from Fort Lee to Alpine, but the occasional scenic vistas between the two points make it more than worth the hike between the two locations. Basically, you'll be keeping the river on your right for the northern approach, which will stay on the "high side" of the mountain all the way to Alpine, and through two separate highway rest stops. Coming upon one of these rest stops is humorous enough, you don't need to carry a lot of water for this hike: rely on the existing sources and carry less.
You should start your hike from just south of the bridge, in Fort Lee Historical Park (part of Palisades Park, and thus inidicated by the park sign) in Fort Lee, NJ. You start just south of the GWB and walk along paved paths, following the aqua-blazed Long Path Trail. The Long Path is one of the oldest nationally-recognized trails in America, incorporated at the same time as the Appalachian Trail. The main difference is that the Appalachian snakes its way through multiple state parks, staying relatively isolated from modern society. The Long Path transverses areas both urban and desolate in its almost 400 mile journey through New York. This is the beginning of the Long Trail. If you followed the aqua blazes north you would (with some luck) reach Altamont in the Catskills. Of course, if you take the path followed in this blog, you'd only reach Alpine anyway. After reaching Alpine (clearly designated by it being the third major marina along the trail and the trailside facilities available), the trail goes south to follow the yellow Shore Trail back to the GWB and the parking lot.
The important thing to remember on the way back is the location of Riverside Park in New York, the series of arches that designates the beginning of the Hudson River outlet on Manhattan Island and one of the busiest urban water treatment facilities in the world. Keep this as your reference point as you go south and you'll be relieved when you see the GWB again (it never seems to reappear, especially on the unforgivably rocky Shore Trail).
If you're feeling particularly adventurous then you can hike the George Washington Bridge either before or after (I'd suggest after) the meat of your hike. Me, I was happy to get into my air-conditioned car and get the hell home after this ankle-breaker.
