Brandenburger Tor, Reichstag, Kanzleramt, Train Station, Potsdamer Platz and Friedrichstraße are all within walking distance of each other, so if your primary interest is in visiting these sights, you may want to stay in that area. Last time we were there, we found it extremely overrun by tourists though.
Kurfürstendamm is the main shopping steet and there are many nice restaurants in the some of the side streets. For many years, the East was the place to be, but it seems things have changed and the Charlottenburg area has improved quite a bit.
You can just get a day pass for the U and S-Bahn and then just take these to the different sections of the city.