ZUM,
What airport in the Philadephia area are you doing this flight from? I flew to Lincoln Park, NJ from PNE through the VFR corridor. Definitely go through it; it's one of the most scenic routes you can take in the world with a small plane.
Make sure you have the current New York Terminal Chart. Study it before you go, because there are frequencies on it that the river route uses.
What I did, and is the best way in my opinion, is to just get flight following up to about a point west of Colts Neck VOR. Then, cancel it and switch to the river frequency. It's either 123.05 or 07, but you'll see them on the chart.
The route will take you over Union Beach, NJ where I was about 1500'. Then you go direct to the center of the Tappan Zee Bridge and cross that at or below 1100'. From there, you head to Governor's Island staying below 1100' at all times, and I'd recommend flying at about 800', which is plenty clear below class B and above the 500' AGL rule.
The view is just incredible. Just remember, if you mess up something just a little bit, it's going to be on the news, you're going to be in trouble, and it could ruin other pilots opportunities for this flight route.
Have fun!