When we went to Berlin we stayed at Camping Sanssouci-Gaisberg in Potsdam. It's a relatively quiet site and reasonably convenient for day trips into Berlin without the caravan. I'd advise leaving the car on the outskirts though and go in by public transport as you now need an emissions sticker to be allowed into the city.
Check here for details. While such a sticker is not costly (only a couple of Euros), it does mean that you would have take your car and registration documents to a German MOT test centre first, once you've entered Germany, as foreign registered vehicles are NOT exempt from the requirement.
By the way, the following cities in Germany have already adopted this requirement:
Berlin
Dortmund
Hannover
Ilsfeld
Cologne
Leonberg
Ludwigsburg
Mannheim
Reutlingen
Schw