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.
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.
My favourite bar of the many around kreuzkölln is Bellman. After its sudden closure and reopening it underwent some changes and is boycotted by some of its former patronage, but for the less principled like myself it’s still a good place to go and they do pull the best Jever in Berlin.
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.