Thats a pretty small niche. Not sure if you will like these but heres a few suggestions I can think of...
Elliott Smith (solo acoustic stuff, not-instrumental), start with Either/Or or XO
Minus the Bear - Acoustics (acoustic versions of their best songs)
Neutral Milk Hotel - In the Aeroplane Over The Sea (indie classic, centered mostly around the singer/songwriter, a lot of acoustics)
Love you Moon - Waxwane (Matt Embree from RX Bandits solo acoustic stuff, a lot of emotion, all acoustic)
The Microphones - The Glow Pt.2 (another really popular indie record)
Come to think of it, I don't know any solo acoustic stuff without vocals, so if anyone knows anything like that I would like to hear it too.