Königssee is a bit of a special place for me. Been a couple of times on the first boat out: both times the weather was glorious (misty morning turning into a warm, bright sunny day). An easy to moderate hike at the bottom end of the lake to Rothbach Waterfall. Cable car to the top of the Jenner close by (photo opportunities)
Tegernsee is also top notch. Bad Wiessee has a long promenade with views. Rottach-Egern has an easy walk by a stream flowing into town. Ferries. Not many foreign tourists on Tegernsee.
Ammersee is fairly easy to reach from Munich. I've visited Andech Monastery on Ammersee but spent no time on the lake. Starnbergersee is the quickest of all to reach from Munich. Walked along a trail from Starnberg to Berg, where Mad Ludwig met his unfortunate end. Both Ammersee and Starnbergersee have a fairly long cruise route (done neither), and both have Sunday brunch cruises.
Last but not least, Chiemsee (just under two hours from Munich). Maybe a bit too far but is home to one of Ludwig's palaces (Herrenchiemsee), as well as the tiny island of Fraunchiemsee (abbey and a couple of restaurants). Flat hiking on both islands.