Visit the Reichstag, escpecially on nice summer evenings. Almost no waiting line and a nice view around the town.
Visit the museums in the heart of the city, eg. the Alte Nationalgalerie, Bodemuseum and Pergamonmuseum. They are also architecturally interesting because they were recently renovated.
Hang out in Volkspark Friedrichshain in summer or go see the Eastside Gallery (preserved part of the wall that once divided Germany and the City)
Go visit the TV Tower ("Fernsehturm") near Alexanderplatz. Excellent view over Berlin, and a revolving café floor.
"Bar for common people"
for things to do check out isango.com or isango.de :-)
Take the cycle trip around the Wall. The Wall Tour from Berlin on Bike - www.berlinonbike.de Bikes picked up from near Eberswalder Strasse U-bahn
there are a few good street markets over the weekend, mostly sundays.
i prefer the Arkonaplatz, small but a good mixture between trash, ostalgia and antiques
Sunday, So 10 – 16 Uhr
Visit the biggest everything -flea- market in Mauer Park every Sunday
The Sundays karaoke in Mauer Park are not to be missed!!