I still think naming the one black kid in town "Token" is the best joke in the whole show. I always like jokes where you're not sure if you're supposed to be laughing or not.
I immediately think of the episode where Butters returns home to fix his anger issues, only for him to be angry about Ben Affleck the whole time. Can't recall any other Hawaii-centric episodes. I love South Park.
So I think it's mostly South Park creators being obsessed with Tiny Tim, and well, who could blame them? Everyone loves a Ukelele. Spongebob clearly takes their musical influences from him.
Not just South Park, in BASEketball there's a Hawaiian luau scene where one of the characters gives a big speech that ends the animosity between the two main characters.