Wim Wenders shot Wings of Desire here. It's a quiet place to work and definitely a gorgeous place to visit. Combine it with a visit to the Philharmonic, just across the street. Affiliation is 30 euros per year and you have lots of desks all over the library to choose from.
There's nothing more revigorating during the dark winter days than spending a couple of hours in a sauna. Germans have mastered the art of sauna and you can find amazing pieces of architecture in the public swimming pools (Stadtbad). I find Stadtbad Neukölln very peculiar in its neoclassic architecture and it's definitely a wallet-friendly option to enjoy some sauna time there. Be prepared to be naked in front of man and woman!
Best record store in Berlin. A great selection of Rock, Folk, Indie, Wave, Industrial and especially the huge floor dedicated to House and Techno Records. Staff are typical Berlin-Style - not very friendly but very knowledgeable.
I never heard about Havel until some friends and me checked out the google earth for a trip at the weekend. We went there in the german winter, oh yes...in the winter. I loved this place because is a small city island with a lake (which was frozen at that time) and with lovely houses and an old mill. I have never been there in the summer but i can imagine how wonderful would be.