I personally would say that Prenzlauer Berg near a U2 stop is close to ideal for a tourist. The U2 itself runs very frequently and even in the middle of the night. It takes you to Alexanderplatz, Potsdamer Platz and Zoo.

If you want to go anywhere else in Berlin S+U Schoenhauser Allee connects the U2 to the Ringbahn, at Potsdamer Platz you can get the S1 and S2, Alexanderplatz offers connection to the Stadtbahn and it is also a hub now for the vast tram network in the East of the city.

In general, I would recommend planning your trips in advance if you have a specific destination in mind. Berlin's public transport network has various branches with the S-Bahn, the U-Bahn, trams and buses. All of those tend to be reasonably reliable (crossing fingers with the S-Bahn) and they are generally well-integrated. A planned itinerary can save you a long time by allowing you to utilise the full range of options of the network. The English language route planner: http://www.vbb.de/en/index.html