Yeah, that's good. No chest hair looks a little prissy to me. Like it's okay if you're a swimmer or something, but otherwise you're trying too hard. As far as I know, pretty much no girls like back hair, so I think you're making the right move there.
Definitely keep the back clean & clear! I am not sure how hairy your chest is, but as long as you keep it maintained and looking good then I think you are set. No reason to totally shave it, there are plenty of females out there that like chest hair.