I don't know how old your son is, but Splish Splash water Park on long Island is nice and also adventure land in Farmingdale on Long Island is good for younger children. lots of lakes around if you like fishing.
Central Park is always good in the summer and even in the fall. If you have a bit older children and it is raining, the Metropolitan Museum is free, or you can donate some cash to them, and then there is the children's museum on Long Island.