I agree that this song is about Jenny's love for L.A. , but I always thought that it talked about leaving L.A. -maybe for touring- and knowing that L.A. would still be there as her home when she's back. Therefore the "you" would be L.A. However, she starts saying "i'm leaving you, I'm going home", and for that reason I think that maybe this is about the end of a relationship -and the "you" would be another person- and that once the relationship ends and she is heartbroken ("With my heart in a sling, tail between my legs a-swinging") and goes back to the city that can heal her.
I agree that this song is about Jenny's love for L.A. , but I always thought that it talked about leaving L.A. -maybe for touring- and knowing that L.A. would still be there as her home when she's back. Therefore the "you" would be L.A. However, she starts saying "i'm leaving you, I'm going home", and for that reason I think that maybe this is about the end of a relationship -and the "you" would be another person- and that once the relationship ends and she is heartbroken ("With my heart in a sling, tail between my legs a-swinging") and goes back to the city that can heal her.