Wernigerode is several hours drive from Berlin, and not only is it the headquarters for the HSB, but it is also a very interesting old German town of half-timbered buildings, an ornate city hall, and a castle up on the mountain top. Too far for half a day, but probably doable as a long one day trip. I usually do it by car, which is probably fastest, but you should also check the train scheds from Berlin. The ride from Wernigerode to the top of Brocken is behind steam, and the top of Brocken provides both a great view and some cold war history since it was a Soviet listening post and the buildings are still there.
If you're stuck in Berlin, don't miss the new main station, or "cathedral to trains" as one magazine called it.
JBW