Some weeks ago the first seats2meet free co-working space was opened in the Boulevard Berlin in Steglitz: https://www.seats2meet.com/locations/635/Boulevard_Berlin. It is located on the upper floor where a lot of the restaurants are and it is facing Harry Bresslau Park.
You get a place to work, wifi and also free coffee in exchange for logging into the local serendipity machine (http://serendipitymachine.com/bberlin/), entering your fields of expertise and being available for knowledge exchange.
Another place where you can work almost for free is the SUPERMARKT in Wedding near U Volta Straße, not far from the Factory: http://www.supermarkt-berlin.net/. They have regular co-working seats which you can book for longer periods of time and also cost something. But they also have a large co-working area in the big even space where there is also a cafe. If you buy something at the bar you get a voucher for the internet. They do not mind if you bring you own drinks and food otherwise, but they do have to pay the rent so they ask for at least one little purchase at the cafe.
There is also a serendipity machine at the Supermarkt which needs to be advertised a bit more: http://serendipitymachine.com/tsmimm15/
BTW, in the Boulevard Berlin there is also a place for young designers to offer their produce and for giving workshops for all things DIY: https://www.facebook.com/pages/PopUp-Village/264936823679810 They are especially interested in upcycling.