From art to history, the museums of Berlin are really outstanding. Here are the ones I visited and recommend:
Neu Nationalgalerie, Potsdamer Strasse 50: This is a must see museum that has a wonderful collection of modern art including works by Leger, Picasso, Dali, Magritte, Kandinsky, Ernst, Munch and Kirchner.
Hamburger Bahnhof, Invalidenstrasse 50/51: Located in the old Hamburg Railway Station, this contemporary museum was opened in 1996. It is host to temporary exhibitions as well as a permanent collection which includes Warhol, Twombly and Rauschenberg. The Rieckballen shows selected works from the Frick Collection in rotation.
Jewish Museum, Lindenstrasse 9-14: This a very attractive museum with displays on the history and culture of Germany’s Jewish community and the repercussions of the Holocaust. They also have a nice cafeteria that is a perfect spot for lunch.
Die Mauren The Berlin Wall East Side Gallery, Mullenstrasse: This one mile section of the Berlin Wall runs long Mullenstrasse between Hauptbahnhof and Oberbaumbrucke. The panels of the wall are painted with approximately 100 paintings by artists and street artists from countries around the world. It is the largest and longest-lasting open air gallery in the world.
Martin Gropius Bau, Niederkirchnerstrasse 7: Used for temporary exhibitions. Check the site for the current schedule. I saw the two favorite shows of my trip here!
Topographie Des Terrors, Stresemannstrasse 110: This museum, with its exhibitions on Nazi terror, was built on the former site of the headquarters of the SS and the Gestapo. It is very interesting to see.
Sammlung Berggruen Museum, Schlosstrasse 1: A small private museum featuring the collection of Heinz Berggruen. The collection contains works by Picasso, Klee and Matisse with a few by Van Gogh, Braque and Cezanne. I enjoyed this museum very much.
Pergamon Museum, Bodestrasse 1-3 on Museum Island: This is one of the best museums in Berlin. It has a large collection of antiquities including the Pergamon Zeus Altar and the Market Gate from Miletus. It also has a good collection of Middle Eastern Art including a reconstruction of the Babylonian Ishtar Gate.
Haus am Checkpoint Charlie, Friedrichstrasse 43-45: This small museum has an interesting collection of memorabilia from the construction of the Berlin Wall and life behind the wall. Make sure to stop at the replica booth at the former Checkpoint Charlie across the street.
Berlin Wall Memorial, Bernauer Strasse 111/119: This memorial contains the last piece of the Berlin Wall with the preserved grounds behind it and therefore, shows how the border fortifications looked. There is even a guard tower. There is a visitor/documentation center with exhibits and a film across the street.
Bauhaus-Archiv, Klingelhoferstrasser 14: Not too far from Potsdamer Platz. The Bauhaus school of art, started by Walter Gropius in 1919, was one of the most influential art institutions of the 20th Century. The group believed that art and technology should combine in harmonious unity. The school provided inspiration for Mies van der Rohe, Paul Klee, Wassily Kandinsky and Laszlo Mohly-Nagy. The Archiv in its attractive contemporary building, houses a library and exhibition halls which feature displays on the history as well as displays of furniture and other objects. There is a nice café to take a break from your walking.
There was a Guggenheim Museum in Berlin which has since closed.