Berlin is a HUGE city. Back in the day you could spend a week there and never see the Wall. Yes, you must go to the Checkpoint Charlie Museum. It's the best and has gotten better in recent years. Also go to the the Stasi Museum:
Stasimuseum Berlin - Forschungs- und Gedenkstätte Normannenstraße
Though it's mostly for Germans and I can't recall if they have English translations. I was last there when it first opened. If you're into bikes, Berlin is where BMW motorcycles are made. Don't know if they give tours.
It's one of the world's greatest cities, but it's so chic and touristy now, I think it's lost a lot of its old world charm. Be sure to rent the dvd's
Goodbye Lenin and
The Lives of Others so you get some sense of what it was like back in the day.
Do try the Berliner Weisse mit Schuess - rot oder gruen. Best local Pilsener is Berliner Kindl, though you can't really go wrong with beer in Germany unless you try foreign beer (other than from the Czech Rep.).