Harriman State Park reaches into the western side of Stony Point and changes the town's feel from commuter edge to rocky Hudson Highlands. The wider park has lakes, ridges, old roads, and a large trail network, though not all of its best hikes start in Stony Point itself.
Use this as the outdoor half of a day here. The battlefield gives you history and river views; Harriman gives you woods, stone, and the rougher landscape behind the Hudson towns.