This is the Nutten Hook Reserve also known as the Styvasent Ice House. The road to get to the park it goes from a small two lane to a single lane road but opens up to a big parking lot with a pavilion. As you are walking to the river look out there are 2 trails, one that takes you to a small beach and the other takes you into the woods. In the woods there is a structor and there is a trail as you keep walking but it was over grown when I went there. Also on the road there, you do have to cross over train tracks so look both ways before crossing.
There is a rocky shoreline you can walk on but I would be careful of snacks or other animals hiding in the rocks. There are picnic tables set up near the water and there is a good size beach that you could set up a blanket. It is a cool structor that you can learn about how they used to cut ice out of the river. I do remember in middle school or maybe elementary going here for a field trip