Great to see some of the tips already here! Now for a few more:
The Andorra Bar, at Münstergasse 20 (near the Grossmünster), has live jazz every second Monday with no cover charge - so, in the next little while, that would be March 22nd, April 5th, April 19th...and so on.
http://www.andorra.ch/
However, for a place that has live music every night, one of the first places that springs to mind is the Casa Bar nearby -
http://www.casabar.ch/ - expensive drinks, but good music and no cover. Not only jazz music, also blues, funk, and other styles.
The previously mentioned JazzBaragge (at mehrspur jazz club) is stellar for jazz music, I agree, and they have fabulous wednesday jams - but if you're looking for a "bar/pub/restaurant"-type atmosphere, as opposed to a "jazz club/music-listening venue"-type atmosphere (if you get my drift..?), I'd perhaps save this one for another time. Your call, though.
Let us know where you end up going, and if you find somewhere new and exciting!