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.
A place where I spend some time almost everyday is the Marheineke Markthalle on Bergmannstraße in Kreuzberg. It's just around the corner from where I live and a great place to buy fresh food and products from local farmers or all kinds of delicatessen from different countries. Many market stalls also sell freshly prepared food and it's always busy at lunchtime. For saturday mornings try the original french croissants.
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.