Music is absolutely central to Mick's story and it is the strongest symbol of hope, beauty, and love in the novel. How's that for clear cut?
Mick's quest for music functions on two symbolic levels. First, music gives us a ton of insight into Mick's character. Mick pretty much is music in a lot of ways, an idea most dramatically demonstrated during the scene where Mick hears Beethoven's Third Symphony.
The outside of her was suddenly froze and only the first part of the music was hot inside her heart. [...] It didn't have anything to do with God. This was her, Mick Kelly, walking in the daytime and by herself at night. It was the hot sun and in the dark with all the plans and feelings. This music was her – the real plain her. (2.1.128)
(Quick sidebar: why wasn't Beethoven's more famous Fifth or Ninth Symphony used for this scene? Well, Carson McCullers was studying to be a pianist at one point, so we don't think her choice here was accidental. Beethoven's Third Symphony is what many consider to be the start of his more mature period – it was the jump-start he needed to later write things like the Fifth. Mick, a kid having her first serious musical awakening, is linked to this younger phase of Beethoven's career. Awesome, we know.)
As a budding musician, music constantly reverberates around inside of Mick; she even relates to the world largely through music. Mick has a song in her head for any situation:
There was a slow colored song in her mind – one Portia's brother used to play on his harp. She pedaled in time to it. (2.11.66)
Take a look at that detail about Willie: at the beginning of this chapter, Mick had a nightmare about Willie in prison. Now, because Mick experiences and understands the world largely through music, it's pretty clear that Willie is still on her mind, even while she's off for a fun afternoon with Harry.
But music does more than just represent Mick's character: it also seems to symbolize how each of these characters is looking for something better in their life, something meaningful. Music is what leads Mick to think about her dreams, but all of these characters have dreams of their own.
Music is a very personal thing for Mick, but it also bring people together, especially the Copeland family:
And after the solitary hours spent sitting in the dark kitchen, it happened that he began swaying [...] and from his throat came a sound like a kind of singing moan. He was making this sound when Portia came.
Doctor Copeland knew of her arrival in advance. From the street outside he caught the sound of a harmonica playing a blues song and he knew that the music was played by William, his son. (1.5.2-3)
As much as Copeland tries to distance himself from certain facets of the black community, and even his own family, his unintentional, almost automatic "singing" seems to betray a part of himself that he'd rather deny, a part that is actually emotional. Both Copeland and his son make the same type of music, too: mournful, bluesy songs.