Or in Joisey - I pay for parking at Ramsey 17 (one of the stops on NJ Transit, about 45 mins from NYC) for $310 a year, I believe. 24 hour access with a card, completely covered, and safe.
Just another option. Though the best is to either keep the car in VA or sell it; you won't need a car up here (especially factoring insurance rates - be prepared for sticker shock). Especially with grad school, you won't have much time.