We stayed at the Arcotel Velvet in Mitte which we both really liked. It was easy to get just about anywhere with the Bahn around the corner and the tram running right out front. Our room was small but seemed more spacious by the lack of internal walls, using just sheer curtains as partitions.
You can rent a "classic" East Berlin relic, the Trabi and take a Trabi Safari Tour of Berlin but we chose to do a lot of walking instead. The best way to start is with a stroll down the grand Unter den Linden where all the embassy's are located (amongst Bentley dealership and high end boutiques) until you reach Brandenburg Gate and the Reichstat (Parliment Building).
Having reached our limit of Communist history absorption for the day we headed to the stunning area of Potsdamerplatz. Crumbling Cold War buildings are replaced in this "new Berlin" area with glass skyscrapers and modern art sculptures. It's a "Time Square" of sorts but clean and modern and inviting. There is a small section of the Wall that you can explore but for the most part this area is about the future of Berlin.
Back near our hotel in Mitte we stopped in at the Kunsthaus Tacheles, an interesting building dating from the early 1900's. Built as a department store, it became a Nazi prison for a short time, was used for some movie shots and was taken over by an artist collective shortly after the Wall came down. It's an interesting space housing all kinds of modern art but they are continually being threatened with evacuation so if you're interested go before it's too late!
Continuing on our somewhat macabre morning we headed to the Topographies of Terror which is located next to a piece of still standing Berlin wall. This use to be the location of the Gestapo, SS and Reich Security main headquarters. Now it's an open air exhibit which gives a timeline overview of the Third Reich.
Ampelmann, which is a beloved character and was actively saved as a reminder of their own style. Besides seeing it on the streets in the East you can find all sorts of souvenirs in the Ampelmann shops.
It's an amazing city and I hope to go back again!
There's many more photos of Berlin here.