There are a number of things to consider when trying to decided where to live in Berlin: vicinity to your job, amenities in the area and most importantly lifestyle and culture of the area.
Charlottenberg, Wilmersdorf and Zelhendorf attract a large expat community. The main concentration of international schools are in this area as are the major universities and hospitals.
Schöneberg provides a sanctuary for the gay community while Kreuzberg and Friedrichshain offer something more bohemian. Both areas offer a great range of accommodation, shopping and recreational choices. However, there are no international schools.
Mitte, Tiergarten and Prenzlauer Berg provide a very chic, trendy lifestyle choice. However unlike other areas, Prenzlauer Berg is renown for its family vibe and as a result there are a number of international schools both on the border of Mitte/Prenzlauer Berg and in Prenzlauer Berg itself. All three neighbourhoods have a strong attraction with expatriates.
While Berlin is a relatively safe city compared to other metropolises. Working class areas in the far East should be avoided, as anti-Auslander (foreigner) sentiments are strongest here.