I'd love to help out as I was in Berlin for the first time over New Year and had an amazing time, but unfortunately most of it passed by in a blur of cheap beer and cheaper speed.
I remember that you can get a day pass for many of the museums in the 'museum quarter' (Berlin's South Kensington, only bigger) that's only slightly more then the entry fee for any one of them. There's a great Lebanese (I think) restaurant with brilliant food, cocktails and shisha near where we stayed in Ostkreuz, in the East End - can't recall the name, I'm afraid.
Anyway, there's loads of great stuff to do/eat/drink, I'm sure you'll have a great time.
Yup, Berghain/Panorama Bar definitely lives up to the hype. Really fantastic sound system, awesome space.
I also went to a place in Prenzlberg called Zurmoebelfabrik when I was over in January - really great bar/club. Lovely crowd, and the closest to laid back 'old' Berlin I got to. http://www.zurmoebelfabrik.de/
Also, check the Jewish Memorial just south of thhe Brandenburger Tor - breathtaking.