I was also looking for inspirational places that are not over-run by tourists, well I was tourist myself but I guess you know what I mean...
Here is what I found...
Day 1 - SUNDAY (shops are closed but there is plenty to see anyway)
First stop - flee market / antique market - simply Troedel Markt! ;-)
Second stop - Wonderful green space (Tiergarten) with a hidden spot to find something to eat.
We took a reasonably long walk through the park but it was definitely worth it. The place where we ate is difficult to access otherwise. You can also rent a rowing boat there.
Third stop - Gemaeldegalerie (Fine Art Gallery with paintings only)
Fantastic Gallery with outstanding collection of old masters and virtually NO visitors while everyone is on the Museum Insel. Remember, art does not always have to be taken seriously. We amused ourselves by searching for funny details in the paintings and there are plenty! Check out the devils, angels or small dogs, they are usually the best...
By the way, do not rely on the cafe in this gallery, there are some basics to eat and coffee is available but it is not great.
Places to eat at the end of the long day can be found inside the Sony Centre at the Potsdamer Platz, only few hundert meters from the gallery (there is S-bahn station too). I can strongly reccommend panacotta in the Keisersaal Cafe. ;-) Great for people watching too!
Here is how to get there: