Wow, it's kinda challenging for him.
But, Hot Mess by: Cobra Starship

I think "Behind Blue Eyes" by Limp Bizkit fits him very well.
I mean sure we could go for Songs like Hot Mess or Monster by Lady and they would fit him great but at the end of the day he's a very broken person and dissapointed and lonely.
So i think that now one really knows what it's like to be Damon Salvatore.
As the words fit the Lyrrics.

White Blank Page, by Mumford and Sons
Don't believe it? Read these lyrics and DENNYYYYY ITTTT! ;)
lyrics:
Can you lie next to her
And give her your heart, your heart
As well as your body
And can you lie next to her
And confess your love, your love
As well as your folly
And can you kneel before the king
And say I'm clean, I'm clean

Chorus:
But tell me now, where was my fault
In loving you with my whole heart
Oh tell me now, where was my fault
In loving you with my whole heart

A white blank page and a swelling rage, rage
You did not think when you sent me to the grave, the grave
You desired my attention but denied my affections, my affections

Chorus

Lead me to the truth and I will follow you with my whole life
Lead me to the truth and I will follow you with my whole life

This song is not only fitting to his feelings about Elena "Oh tell me now, where was my fault in loving you with all my heart?", but about his constant rejection by Katherine "you desired my attention but denied my affections", and his brother being the one to turn him "you did not think when you sent me to the grave"
Oh gosh, Damon's entire story just makes me cry.