Organize a guided tour of Marie-Elisabeth-Lüders-Haus and see what it's like to walk the halls of power. You'll get an interesting peek into local politics.
You'll be spoiled for sightseeing choice when in Mitte. Marie-Elisabeth-Lüders-Haus is a good place to begin here, but there are loads of other worthy places to consider. Alexanderplatz, Brandenburg Gate, and Reichstag Building are close to the modern government building and will fill in your day nicely.
