Went there end of last year, it was a great place albeit it has a very strange vibe.
The best museum of the lot that I went to was without doubt the DDR museum (as
@bigjonny mentioned), it manages to be very educational and really interactive. The Neues museum is also a must see, if for no other reason than the bust of Nefertiti which is the single most beautiful object that I have ever seen in my life (and photos do not do it justice). Next door to that is the Pergamon museum which is also really good. All these are on or near Museum Island so you could do them all in a day.
The Neue Museum combines related exhibits: This joint exhibition allows visitors to trace the development of prehistoric and protohistoric cultures.
www.smb.museum
The Pergamonmuseum houses three collections: the Antikensammlung, Vorderasiatisches Museum and the Museum für Islamische Kunst.
www.smb.museum
The Spy Museum would also be worth attending, if you want Cold War related things - it is also quite interactive, but not as good as the DDR museum:
The German Spy Museum Berlin gives a unique & interactive insight into the history of espionage. Click here for more information on the capital of spies.
www.deutsches-spionagemuseum.de
I actually stayed near Checkpoint Charlie, which a lot of people did go to but it is basically a hut in the middle of a road surrounded by shops selling tat and a McDonalds, so I wouldn't say it was worth going out of your way to. It is near to the Mall of Berlin though which, as malls go, was decent, and the architecture around there is all old East German apartment blocks which are interesting of themselves.
The only other place I really liked was San Souci, which is just outside of Potsdam - its like a sensible version of Versailles, two palaces set in a lovely park. The second (newer) palace is (or was) only accessible with a tour group, but you can book tickets on the day and they'll show you all the good bits.
Food wise, I must confess I thought Cologne was a lot better in that respect.