If you feel inclined to take a relatively easy "hike" (if the undemanding walk can be called that), the Old Croton Aqueduct Trail is a good, public-transit-friendly day trip from NYC. Jump on the Hudson Line at Grand Central and get off at Ossining; there's a five- or six-mile stretch that you can take to Croton Gorge Park, where you then double back to return. Poke around the Croton Gorge Unique Area if you have a bit of time; you descend to a lovely, relatively quiet stretch of river that you can dip your feet in.
