When we stopped in NYC we stayed on Statten Island on a mooring ball at Great Kills. We then took the train to the Statten Island Ferry - the best free boat ride in the USA - and the subway to Central Park. One transit ticket covers you for the train and subway in one direction, North or South.
The cost of a mooring ball was $25 per night or $100 for the week. They also have launch service which will pick you up and deliver you to the dock free.