To answer your question-

Not sure exactly where you are looking to park in Fort Lee but the Doubletree will work. I've had friends park there from AM till AM the next morning without any problems. I can't vouch for a Friday till Sunday Afternoon park but my friends didn't have any problem Sat. morning till Sun. morning.

I do not agree with Blumie and RooseveltL about plenty of places to park for free in NYC. Yes, there are spaces but that can mean looking for a long time and getting lucky. Plenty and easily are two words that don't come to mind when I think of parking spaces in Manhattan. Perhaps they can give 4 or 5 locations since its easy and plentiful to help you out.