For accomodations that are also a lesson in East German architecture and interior decoration, grab a bunk or a room at the DDR-Ostel, right next to Berghain and an important subway and streetcar terminal in East Berlin. 

Take the S-Bahn westward to Alexanderplatz, and wander around this famed city-square/transportation hub and grab a very fine espresso and pastry in the courtyard-refuge of Father Carpenter a couple blocks away.

Then visit Fat Tire Bike Tours and inquire after the times of the tours along the former route of the Berlin Wall. If it's happening in the morning, go ahead and get this unavoidable ritual out of the way, but if not, head on foot to the Museuminsel first. If there's only time for one museum, the Neues Museum is the best choice for the architecturally inclined, where one can marvel at the visible traces of its prize-winning reconstruction.

For lunch, visit the Prinzessengarten in Kreuzberg for a tasty, organic and locally-sourced lunch at a restaurant that is also a community garden. 

Pick up the U8 right next door and take it to Leinestraße, where you can spend some time wandering around the giant expanse of Tempelhoferfeld, one of the city's more peculiar, but most characteristic, urban development projects.

Pick up the S-Bahn on the other side of the field and take it all the way to the Greifswalder stop, and enjoy this slow, above-ground ride through many of Berlin's Eastern districts. 

Once back in Prenzlauer Berg, wander around slack-jawed among the Soviet apartment blocks, particularly the Ernst-Thälmann-Park complex to the South. If so inclined, push even further outwards to the Weisensee or further inwards to Volkspark Friedrichshain.