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!
This cinema is nothing special if you're looking for that comercial combo big screens + major sound system, but it has its own sidewalk charm and decadent glam. Also it makes a good option for a date. You have plenty to choose for dinner and drinks all around Kottbusser Tor.
It is the highest place in Berlin and is made of wartrash. Translated Teufelsberg means "Devils Mountain". The whole area always reminds on how beautiful Berlin is: On one side you see the big city and when you turn around pitch black forrest.
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.
While strolling around Mitte, check out the flagship store of Berlin´s cult women fashion brand. (And try a delicious cinnamon bun at Zeit für Brot next door.)