Brewer's Berlin Tours are a great way to experience the city of Berlin.  Their walking tours have several themes, depending on what your tastes are.  You can take the day long Best of Berlin Tour which will give you a a great overview of the city, or you can target your specific interests with the tours that target Jewish and Nazi history in Berlin (the Third Reich Tour) or the Potsdam Palace tour, or their fun Sinful Berlin Tour.  For those on a budget, they also offer a Free Tour of Berlin, with tips greatly appreciated.