There is so much to see in Berlin that GCTdoes not take you to. I'm going to list a lot of places that you can see. Also, I googled Berlin Tours, go to Berlin-Tours.net. You don't have to take a tour, just look at the site and open the tour packages to see what there is to see in Berlin.
My husband and I were in Berlin in 1962, 4 months after the Wall went up the first time. We were young miitary family from Heidelberg, so did not have a car. We walked and walked, but saw a lot. We went back in 1975 for a square dance festival, and by that year, the military were able to tour part of East Germany and East Berlin. There is now a hop on and off bus tour you can take.
Where Einstein lived, where JFK delivered his famous speech; Charlottenburg, Schoneberg and Tiergarten castles. The Victory Column-see Wikipedia for all kinds of interesting information on this famous column. Where it is located, it was on a long boulevard with trees on both sides, and we walked so very far to see it--have to see it from afar first, then walk up to it and even go inside climb steps.
See the Kaiser Wilhelm Kirche (church) -the steeple was blown off during WWII, sat crumbled beside the church which was saved and they vowed it would be placed on top of the church when East Berlin (and Germany) was reunited with West Germany. Later, I understand they decided not to put the steeple back on. It is a memorial to the devastation to WWII. You can go inside there is a chapel.
The memorial to the Berlin Airlift at Templehof is noteworthy - if I find more on it I will post another reply. This is all in what was West Berlin. See http://www.german-way.com/airlift.html and read about the airlift in 1948--Allies flew in food, gasoline and humanitarian supplies to West Berlin because it was blockaded by Stalin after WWII. Interesting article, it is the first one on that site.