For historical reasons there is no conventional city center in the geographical center of Berlin as known from other major cities. Rather, there are several smaller centers in the various districts. There are bigger shopping areas around Bahnhof Zoo and Kurfürstendamm and also around Alexanderplatz and Hackescher Markt. From your accommodation those larger centers you will need between 40-50 minutes by public transportation.
The nearest district center to the university and your accommodations is in the district Steglitz around Schloßstraße. This shopping area can be reached by public transportation within 25-30 minutes (bus/U-Bahn/S-Bahn stop „Rathaus Steglitz“).