Newburgh is a bit better than Normandy Farms for touring NYC, but it's still a good ways out and you'd still spend a few hours each day you're in the city getting there and back.
Croton Point or Liberty Harbor would make more sense for the NYC part of the time, Liberty Harbor particularly for the city proper. I would pack up and move between the Hyde Park area and the NYC area sites. I will also add that I tend to do very little to set up and break camp, so moving around is not too big an ordeal for me compared to some other RVers who prefer to set up and enjoy their outdoor mats, grills, gazebo tents, chairs, pink flamingos, etc.