A very good reason to travel West: the C/O, next to the formerly infamous Berliner Zoo tube station, is an awesome museum dedicated to photography and visual media. Previous exhibitions include Larry Clark, Martin Parr, Anton Corbijn, Annie Leibovitz and Stephen Shore.
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.