Each and every Wednesday at a place in Noord called Old Dutch.
Owned by a very cool gent named Jon from Holland, the house band does an acoustic jam, all comers welcome.
Or just go hang and listen. The place starts to really fill up about 11-11:30, the musicians are excellent.
By 12-12:30 it's standing room only, and considering it's full of locals, THIS is the place to hear the real musicians on the island.
There is a place called Rhythm & Booze that has acoustic music on Thursday, Friday & Saturday. It is located in the alley next to Hooters in the high rise area. We checked it out on a Friday night and seemed to be local musicians. Also, club Chaos downtown near the Renaissance has live local music every Saturday night. I have not checked it out yet but sounds good.