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!
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.