Rixdorf is definitely my favourite area of Berlin, because it is a historic village within in Berlin. At the moment it is under heavy construction, and I found this strange, nearly taken-down building sitting in the middle of the quaint neighbourhood.
Flughafen Tempelhof was once the symbol of nazi-pride when Hitler notoriously comissioned construction of the smallest duty free shop in the world (and a beautiful example of fascist architecture). After the war, Tempelhof became one of the frontiers of the cold war with the U.S. battling the communists (who undoubtedly wanted to get rid of the small duty free shop altogether) via the Berlin Airlift. It turned out to be a huge succes, and enabled the allied forces to remain their presence in Berlin and save the small duty free shop. The real free-market victory will come in about two years though, when project developers will take over and start building houses, blocking my view onto the airfield.
It's an indoor market, which makes it a great option in winter if you are looking for anything from kitsch to classy. I like it because you find lots of old objects that transport you to the past.