The jazz scene is happening for a city of that size, lots of creative musicians, most notably the Bad Plus, Happy Apple, Anthony Cox, and Fat Kid Wednesdays.
Check out the Monday night jam at Jazz Central Studios, 407 Central Ave N - that starts at 8:30. http://jazzcentralstudios.org/
Steve Kenny plays at the Artists' Quarter on Wednesday nights, early show (7 pm), and he always lets people sit in.
Also check out the jazz series at the Icehouse on Nicollet Ave. There are two sets of music on Monday nights starting around 10 pm.
Hope your trip goes well!