A place in the Niederdorf does really nice shows. Its called Cafe Henrici. What do you play? They usually have something between professional and semi-professional acts, but they don't charge a cover and its a very relaxed nice place to play. I played there once and it was great.
Also, there is a venue called Cafe Für Dich or something like that. They do some small coffee-shop style shows.
Have you done this a lot or are you new to performing?