Don't rely on lake option too much. There are a thousand lakes in deed but it's difficult access to them because of two reasons - 1)private property; 2) in most cases shores are very swampy.
But still you can find public swimming places around Jämsä (at least we managed it). Two of them:
https://www.google.lv/maps/@61.87036.../data=!3m1!1e3
https://www.google.lv/maps/@61.99517.../data=!3m1!1e3