I can recommend some things, you can see what you are up to:
When you are in the city, going for shopping would be the KaDeWe, the largest department store on the European continent, or along the Ku'damm (Kurfürstendamm).
Check out the Potsdamer Platz and the Alexanderplatz. Then you can go to the "Regierungsviertel", that's where the Chanceollor's office and the Bundestag are located. Nearby are the Brandenburg Gate and the Holocaust Memorial with a entry-free museum. And the Hotel Adlon is located there as well, which is where Bono ususally stays at.
Museums are mostly located on the Museum's island which is near the Alexanderplatz. There you can also find the Palast der Republik (Palace of the Republic), which is currently being deconstructed.
And check out the former eastern part of the city to see the differences.
In the evening you may want to visit the Bergmannstraße in Kreuzberg. There are lots of cafe's and restaurants, not too expensive,but with an amazing atmosphere.
Berlin has a lot of parks, like Tiergarten in the city. Also the area around Wannsee is great, and you could visit the House of the Wannsee Conference which is entry free as well.
The Zoo and the Aquarium are really beautiful, and since Knut has grown a bit it's not too overcrowded there anymore. He is out all day now.
Beautiful walks you may experience in the Grunewald, and in Potsdam as well. Potsdam is the neighbouring city, but with bus tickets you can go there as well. Especially the parks around the Glienicker Bridge (where the Russian and Americans swapped spies) are beautiful, but huge.
I especially love the Peacock Island. You can get there from the Wannsee.
If you want to swim you can do that in one of over fourty lakes around the city. The Strandbad Wannsee usually is very overcrowded, so you should go for another lake.
You'll find bars and clubs just about everywhere, and we even have some Irish Pubs. I just would not recommend the Hackescher Markt, as this is too much of a tourist trap.