Starnberg: Easy access to the lake. Nice little cafe to the left after the tunnel. Nice area at the Seegartien to the right. Catch "Der Schiff" to take a quick 1 hr trip around the lake. Walk past the Seegarten. Nice area.
Possenhofen: Nice swimming area.
Tutzing: Nice walk to the lake (pretty hilly) . Lots of Bavarian style Biergartens and a nice Monastary.
In general the water is very clean. Since my place in Texas has a spring fed river, I never thought it is too cold to go swimming during the summer.