If the weather's taken a turn for the worse, why not head to Heimatmuseum? You'll be surprised just how many interesting facts you can learn about days gone by here.
This collection of historical artifacts is located in Treptow-Köpenick. Once you've explored everything you can at Heimatmuseum, have a look at nearby Mueggelsee, Kindl-Buhne Wuhlheide, and Köpenick Palace.