Most metered spots in Fort Lee are free on Sundays, but not Saturdays. I'm pretty sure you do need a permit to park overnight on the street.

But I agree with Blumie and RooseveltL. Unless you're really resistant to paying the GWB toll, the time spent parking in Ft. Lee and taking a bus into Manhattan will almost certainly be greater than the time spent looking for street parking in Manhattan.

Go to http://nyc.bestparking.com, put in your arrival and departure times and click the "street" radio button near the top of the screen and it'll show you a map of which streets have free parking for that duration in Manhattan.