You can grab a coffee or a juice right next door to the KINDL Center in the old brewing Hall at König Otto, complete with all the fascinating brewing equipment from its completion in 1930 it is a hall reminiscent of German Expressionism style… or as stated on their website. :)
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.
A very nice little second-hand bookstore, including a shelve with international books in French, English, and Spanish too. Always nice people to meet and a great selection of art and cook books, for affordable prices.
Tuesday's lunch hour tip is the amazing Berlin Philarmonic. A short-duration concert (around an hour) happens every Tuesday at 13h, for free. People make the Philarmonie's foyer full, sitting on the stairs, on the ground and everywhere around. Little advice: bring with you a little cushion for more comfort and try to arrive early to find the good spots.
My favorite lake to visit during the warmest months. It's located in the southwestern part of Berlin and it's reacheable by public transportation, just around 40min from the city center.