Public pools would be more under the jurisdiction of individual towns, unless they're part of the New York State system. You'd have to target the town in which you'd like to swim, then go from there (for instance: in Fishkill, there's a large water park called Splash Down, with numerous pools, slides, water rides, etc.) But even if you're in Putnam County you can go to Bear Mountain State Park, right over the Bear Mt Bridge (it's actually in Orange County), where they have an enormous pool which is open from June until the beginning of September. It's $2.00 for adults, $1.00 for kids, and no charge for kids under 5. The park also has a large play field, a lake where you can rent rowboats, a Trailside Musueum and Zoo, and great hiking, and biking trails. The view from the top of Bear Mt. is spectacular!