Widder Bar - A bit upper class menu prices, nice atmosphere. Outside the concert seasons you often find free tables without reservation. Single musicians play the grand piano then for no entrance fee, sometimes, on Saturdays (not sure about the frequency because concert season is just starting).

Jazz Bar Casa - Opens at 5pm, live music at 9pm. No entrance fee but higher prices during concerts.

Moods im Schiffbau - Not only a bar, but Zurich's Jazz Club. Blues, Jazz, Funk and more, nearly every day of the week. I like it!