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