I like walking around, looking at cool architecture, historical shizz, parks etc, good clubs/music bars.
In which case, I would make Alexanderplatz my starting point, and just meander in the direction of the Brandenburg Tor, stopping by the Rotes Rathaus, Nikolaikirche, the Berliner Dom, the museum quarter, on the way to Unter den Linden.
You will cross Friedrichstrasse, which you will want to turn down as part of a detour, as well as seeing more stuff than you can possibly stop at.
My favourite city in the world. Have fun.