I was there this summer for a few weeks, so I had some time to scope out a few "undiscovered gems":

The Anti-War Museum - http://www.anti-kriegs-museum.de/ - founded after WWI, run by the grandson of the founder IIRC, he gave my friend and I a personal tour of the museum that I will NEVER forget, this is a great place, though not in the best part of town.

The former Stasi HQ (http://stasimuseum.de/) - you can sit at the same tables where DDR security bureacrats made world-shaking decisions. Also plenty of DDR relics, which really allow you to get a "feel" for that time period.

Make sure you also check out the Reichstag, the Prussian Summer Palaces and Gardens in Brandenburg, Ku'damm (Kurfurstandamm) for good shopping, the TV Tower (the crowning achievement of the DDR), Checkpoint Charlie, Brandenburg Gate, Potsdamer Platz, the German Historical Museum, and, if you're up for it, famous "museum island." I think the German Technology Museum is pretty good, too, but I'm not sure, because it is closed Mondays (oops!).