I have driven into NYC while living in DC and RI numerous times. It's not that hard. And I think it's preferrable to parking in NJ and take public transport. Just ask the hotel for good directions, arrange for parking if necessary, and drive there. Yes, it'll cost quite a bit for parking, but you still have to pay for parking in NJ.
Plus, I'd be worrying about the car for leaving in a lot in NJ for 7 days, except at Newark Airport.