there is a jazz festival on tomorrow night from 18:00 - 01:00 all over basel, there is a paper with info about it going around. Also the Kuntsmuseam and livingroom fm are having a music festival at the moment, I was there tonight at it. It's at the Kuntsmuseam and is free entry, really good night
Here is the link for the schedule and list of dj's music is good. The main Dj starts at 20:00 tomorrow and it is open until 07:00 On saturday morning, defo worth a visit, musically and visually it is great.