Most Jerusalemites know about the Jerusalem Wine Festival in August, and the Festival of Lights and Chutzot HaYotzer in the summer, but my favorite of Jerusalem's festivals is the one this week, The Sounds of the Old City Festival, March 20-23. It's a great chance to wander through the Old City and enjoy an amazing variety of all sorts of ethnic music.
You could stand at the Jaffa Gate and hear some classic Ladino music, move a bit further for American blues, to the Cardo for Yemenite rock, and to the Hurva Square for lively klezmer. Or whatever happens to be playing at the time. It's all free, performed by Israel's best musicians.
You can click here for the performance schedule at each spot, or view the whole schedule here, but my advice is to just pick a night and go wander around the Old City and enjoy its sounds. From 7PM to 11PM each night.