i lived in three different flats in goettingen and would be happy to offer tips on specific places. I'd stay away from places near the train station - although the rent is cheap, i had very noisy neighbors and lots of problems there. My single room with a kitchen at Studentenwohnheim Albrecht-Thaer-Weg was really nice, clean, quiet, affordable and just a few minute bike ride from the uni sports complex, for which a membership is like 5 EUR/month. I've also used wg gesucht, but found my ATW sublet through the university appt search website here: http://www.uni-goettingen.de/de/61916.html
feel free to ask any more question about goettingen! i loved my time there!