I've been looking at photos of the Bergmannkiez district in Berlin's Kreuzberg area. The streets look really nice with older renovated buildings. One article I read said the area wasn't as damaged as most Berlin areas in WW2. Looks like a nice area to explore for someone with a fair amount of time to visit Berlin.
I visited the area on the recommendation of a former resident of Berlin as a place to see "Old Berlin" due to the lack of bombing you mentioned. It is a really nice area to wander. There is an organic market on Chamissoplatz on Saturday mornings. There also is also a really cool old brick water tower (DTK Wasserturm) near Chamissoplatz.
Kreuzberg is counter-culture. It was a working class suburb before becoming part of Gross-Berlin. I finally went there in 2007 to fulfill my curiousity of the place, only once...lots of tagging, at least those were the streets I saw...but that was also 2007. Don't expect Kreuzberg as a suburb to be like Charlottenburg.
That area is Western Kreuzberg, which is more upmarket than Eastern Kreuzberg which Fred is talking about. (East Kreuzberg, during the Wall era, was Turks and grubby anarchist squat-punks... it's now mostly Turks and well-paid "creative industries" types who like to pretend to be grubby anarchist squat-punks.)
I find Bergmannkiez more reminiscent of the area around Kollwitzplatz in Prenzlauer Berg than the eastern part of Kreuzberg, which is as Philip describes. I think Chamissokiez is considered a subsection of Bergmannkiez (either that or its neighboring Kiez to the south). The area immediately around Bergmannstraße has lots of shops and restaurants; Chamissokiez is more residential (but nonetheless charming and interesting to see).