I did this exact thing last summer...

...and I'd be happy to share my info with you. I stayed in Prenzlauer Berg (East Berlin) and attended a school called GLS Sprachenzentrum. They teach the Goethe curriculum but at about half the price. I did the intensive course and was in class 6 hours a day, which actually left me plenty of time to explore Berlin and do a few auditions. I stayed with a great lady whose spare room had a piano. She takes boarders from the Goethe Institut in July/August, but in June she usually finds someone independent of Goethe. I can give you her email address and let her know about you if you like! If you have any further questions about GLS, let me know. Viel Spass!