Visit the Stasi (secret police) headquarters. It's really interesting (tragically, exhibits described only in German) and eerie to think what went on there.
Have a coffee at the rotating cafe on top of the TV tower in AlexanderPlatz. On a clear day, you get a great panoramic, 360 degree view of the city and it's spectacular at night.
Quick Tips:
Go early in the year. It's VERY cold but the tourist sites are really quiet. When the sun comes out and you get a clear blue sky it's a glorious contrast for photos.
Just walking from the West to the East is a fascinating paradigm shift, as the buildings and street transform into the ugly Sovietesque creations of the 60s/70s. It's hard to believe East Berlin was the showcase of the Soviet bloc! Alexanderplatz is a particularly ugly yet, in a strange way, attractive part of the East city.
Visit the Reichstag (parliament building) and ride free to the roof where you can peer in and see parliament in session!
Best Way To Get Around:
Yet again, public transport is efficient, fast, cheap and clean. The buses, S-Bahn (overground train), U-Bahn (underground train) and buses are a great way of moving long distances around the sizeable city.
Of course there's no substitute for walking around, and Berlin is a city friendly to pedestrians (as long as you stay away from the traffic nightmare at the Brandenburg Gate.