I would also suggest thinking about
- Postdam (Sanssouci, Dutch Quarter (Holländisches Viertel) or the russian colony. Reachable by S1 or regional train RE1)
- Wittenberg (with the church, where Martin Luther hung his theses. A nice little town, take the RE5 from the Hauptbahnhof)
- Sachsenhausen (for a impressing reminder about the darkest part of our past. Trains S1, RE5 and RB12 go to Oranienburg, from where you may find hourly busses to the Konzentrationslager. Or walk the 2 km)
- Spreewald (UNESCO nature reservat, go to Lübbenau by regional train (RE2) and take a guided boat tour or paddle by yourself. There should be english speaking boatmen in Lübbenau)

I wish you a pleasent trip to our capital!