An area of central Berlin steeped in pre-WWII buildings and Bohemian mystique, Prenzlauer Berg is one of the more notable entertainment destinations for those who may have had an overload of Mitte's museums and mega-squares. Located just east of city center, head here for the neo-Gothic Gethsemanekirche (famous as a meeting place for anti-GDR leaders), a trendy cup of coffee or, you know, the typical sprawling former brewery known as one of the biggest nightlife destinations in the city (KulturBrauerei ).
An artist's haven and a popular settling place for younger expats, you'll find a good selection of establishments along Schönhauser Allee and in the streets surrounding the nearby Helmholtzplatz. Highlights would have to include the oldest beer garden in Berlin, Pratergarten on Kastanienallee, the aforementioned KulturBrauerei, and a number of retro/classic bars like Zu Mir oder Zu Dir on Lychener Strasse, Frannz Club on Schönhauser Allee, and the strangely awesome Dr. Pong (yup, ping pong is king here) on Eberswalder Strasse.
As far as cultural institutions, you'll be lacking for the usual options found in other neighborhood, so if you want to put Prenzlauer Berg on the itinerary, we suggest saving it for evening and later.
Note:Prenzlauer Berg is also quite family friendly, with numerous smaller public parks and playgrounds that have been built in response to the baby boom that has occurred in the neighborhood in the last few decades.