I'm honestly torn between two of them (by the same band, actually).
[video=youtube;TzY3X9aZVPU]http://www.youtube.com/watch?v=TzY3X9aZVPU[/video]
It's important that I designate Floor Jansen's performance of this song, because she absolutely nails the emotional conveyance of the song and can belt amazingly well.
For those who can't figure it out - that's "Ever Dream" by Nightwish.
I believe that captures Hinata's character fairly well.
The other was "Rest Calm" - aslo by Nightwish:
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Since I can only put one video in my posts - that one has to be merely a link.
The overall theme seems to imply a sort of suicide or sacrificial context - but the chorus is what really seems to connect to Hinata's character, for me.