Kw is a great art institute situated at the backyard of a very eastern part of town, place for many other small galleries. Auguststrasse is worth the walk and Kw is worth the stop.
On a leafy street in Kreuzberg is Kuratiert, a contemporary illustration gallery and shop selling prints, ceramics, textiles and more by some of the best creators from Berlin and the world. It also hosts regular dedicated exhibitions, and is a great place to browse for gifts, or just inspiration.
One of my favorite sophisticated-but-casual places in Berlin. Everything is delicious and the restaurant is cozy and minimal at the same time. It is the right place to have a wonderful dinner with somebody special without being too anxious about the dress code :)