There is a beautiful public beach at Mirror Lake in Lake Placid; excellent swimming hole by Jay’s covered bridge, and several secluded swimming holes further upstream near Upper Jay and Keene. Lots of rocks and flat ledges, many deep swimming holes, slide down falls make for a fun-filled day on Ausable river.
Good swimming is in Schroon River at North Hudson Town Beach, as well as Town of Newcomb sand beach with 3,500 feet frontage on Lake Harris. Also in Mill Creek Recreational Area near Lake George and Cedar River near North Creek (sandy beach and picnic spot).
The list of beaches in Lake George with opening/closing times and fees can be found here
If you are in for a competition, Lake Placid offers a two-loop swim as part of its annual Ironman course.