The Pergamon altar and the Ishtar Gate - in adjacent museums in the Museumsinsel, not very far from the Television Tower. They are awesome ancient monuments. The TV tower is hugely over-rated - I'd say go up it if the queue is small but don' bother if it's going to mean waiting ages.
Checkpoint Charlie Museum
Schloss Charlottenburg area museums and art galleries.....but my advice depends on you likingmuseums and art galleries....