I spent two new years eves in Berlin and IMO the best party place is the Strasse des 17. Juni, it's a huge broadway that is packed full of party people (500k+), lots of public cafes, beer, champagne, good food and bands/live music at every corner, and of course there will be a huge professional fireworks display.
Basically the whole city will be one huge party place, Kurfürstendamm (one of the centers of Berlin) usually is crowded and boasting with activity.
We call new years eve "Silvester", btw.
Oh, and it should be noted that many Germans (myself included) are pyrotechnics freaks... there will be a lot of private fireworks as well so it probably can't hurt to wear a cap or hat...
If you want to shoot some fireworks yourself, buy the German stuff from companies like Weco, Nico, Comet or Zink, much better than Chinese import crap. Fireworks will be sold from 28th of December until noon 31th, you must be 18 yrs or older for class 2 stuff, class 1 is kids fireworks.