This place is like being in the Canary Islands, where my hometown is. The wonderful botanical garden has around 22.000 different plant species. I can find here all the tropical species from the island where i grew up: birds of Paradise, palms or dragon trees.
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.
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.
The Tempelhof Airport is now closed and they have transformed the landing field into a public park area. As soon as you go there you notice that usually you don't get to see that much sky in the city so entering this area for the first time is quite overwhelming. I especially love the old softball fields that have been built during the American occupation.