I am in NY every Wed. and drive a van with Commercial plates so I pretty much can park anyplace I like. Parking lots are expensive and the cabs aren't cheap either. You may want to park in NJ and take the Ferry Across.
Check out Waterways. They use to have buses that would take you around after you got off the ferry. I'm not sure how they operate anymore.
Here is their link
http://www.nywaterway.com/

Have Fun,
Barry