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.
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.
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.
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.
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!