What are your characters' tastes in music? Musical tastes can be used to designate class (or lack of, you decide what's appropriate here!). What would win other characters' approval or disgust? What does everyone listen to in your created world? What do they avoid? Is there any crossover with the music we know and love/hate here?
Is there an underground music movement (especially if the mainstream is tightly controlled by the authorities)? Music has always had its rebels (Beethoven and Mozart were there long before punk rock!) so how would your world show this? Do they get away with their rebelliousness?