Parking for trip to NYC?

I am driving from upstate New York to NYC next weekend. Marriott wants to charge $55 per day so I would like to park and take the train into downtown. Where is the closest, safest place to park? It seems that Jersey City would be the best bet for me but I do not know if there are accomodations, if there will be open spots or where are the transit facilities to get me onto the island. Should I just suck it up and pay the fee?