In 1996 I visited Berlin for the first time with my father. He has left that city in 1934 and until our visit hasn't been back. Although he was already 83, we walked everywhere together and he showed me his Berlin. Since then, I have returned many times, and here are some of my personal recommendations for things to see and to do in the city.
1) Staying-- I prefer the West, specifically the area around Ku'damm (short for Kurfürstendamm). It consists of the main shopping streets, and the Tauentzienstraße and Fasanenstraße, which are adjacent to the Ku'Damm. There are many small pensions in that area which offer a good room, with a lovely breakfast for a decent price.
2) Walking--- is one of my favorite activities in Berlin. The area of Ku’damm is also within a walking distance to Potsdamer Platz and even to Mitte through the beautiful Tiergarten.
3) Touring by bus-- The number 100 bus is a great way to see the city and to get to the East side. Its route was created after the reunification of Germany and it connects East and West Berlin passing through many of the sightseeing attractions.
4) Museums--From the more well-known ones I always go back to the Gemaldegallerie which is beautifully planned, and to the Egyptian museum with Nefretiti sculpture.
5) Other favorite museums--A. The Berlin Musical Instrument Museum,where you get to hear the different and unusual instruments being played through the audio guide. B. The Kathe Kollwitz Museum which has the largest collections of works by the German artist Käthe Kollwitz (1867–1945). C. The Bauhaus Archive Museum of Design, which has art pieces, items, documents and literature related to the Bauhaus School. D. The Bröhan Museum which is devoted to Art Nouveau, Art Deco and functionalism
6) Short excursions-- A. To the quaint historic town Kopenick, which is situated at the confluence of the rivers Dahme and Spree in the south-east of of Berlin. B. In Wannsee, The Lieberman Villa: the house of the painter Max Liberman is a lovely destination.
7) Food-- In Berlin I usually eat Vietnamese food, which I hardly get in Israel: Pho, Summer Roll, and Banh. Vietnamese restaurants are usually very good, they are everywhere and are inexpensive. I also recommend the pizza and the atmosphere at 12 Apostel, there are two locations in the east and in the west, they have a lunch special.
In the photo a sculpture by Kathe Kollwitz