Adam Young, the guy behind Owl City has made albums under different names, including his own. One of the bands is Port Blue; he made an almost purely instrumental (only vocals are the first few seconds of the second track) album called The Airship. It feels rather experimental, but I use it to calm down. The other works are under his own name: Apollo 11, Project Excelsior, and Voyager 1.
All are well made and they tell a story through the instrumental music. Would recommend.
If I'm looking to maximize my relaxation, then it's hard to go wrong with Sleepy Fish. Chill beats all the way.
If you want acoustic guitar playing that you probably never experienced before, then check out Alan Gogoll. Love his stuff. Always nice to listen to. His song Mulberry Mouse is a favorite of mine.
Aether also has a few instrumental albums. Eshajori is a very melancholic feeling album. Gives me a lonely, empty feeling, but I love it all the same.
In a completely different direction, but you could check out The Glitch Mob. Definitely electronic, but I wouldn't say EDM.
That's all I have on my phone at the moment. Hopefully these are good starts.