A place that I liked very much in my few days in Berlin,w as the Kulturbrauerei (a.k.a Machineshaus or Kesselhaus). It's a place with good live music. There are some monthly magazines you can check for gigs in that month. (ask you hostel or hotel.)
The Pergamon-museum is a good museum to visit if you are interested in Greek history, and history and art from the Middle-East. I think that seeing the Reichstag (damn what is that dome ugly), the Brandenburger Tor and the Holocaust monument has to be on the list. These are close to eachother so easy to see on a morning. Alexanderplatz is a must see, but a lot there is not to see. (the TV tower, the little church and the Red Cityhall). but you can walk to the nearby Museum Island, and the Dom. I found that Berlin is a good city to walk around in and discover the less obvious things.
There was a concentration camp near Berlin, and I know it's open for the public now, but when I was there I had a discussion with some Germans about it, and they thought that too much was changed, and a visit was not really worth the effort. Instead a visit to the Jewish-historical museum is supposed to be a better trip. (pretty far from the center.) If you have the chance to get to Krakow, than Auschwitz would be WWII-concentration camp that I would prefer.
It has been a while since I've been in Berlin, but I thought the mulitple day passes were alright. Berlin is a huge city and a lot of the sights are pretty far apart, so you need to use public transport pretty much. I would keep away from the BerlinCard, which also has a couple of days of public transport, but also reduced prices for museums. For me these card often offer free entrance of reduced prices for things I don't want to see, so I am usualy better off with 24-48 or 72 hour cards for public transport. (Ooh and keep in mind, and if you buy a daycard for public transport in Berlin, they mean a DAY card, and not a 24 hour card.)