Repetition and Meditation
A big reason I still play instruments is for how genuinely soothing it is.
When learning a technique or a piece, it's unavoidable: There are some things you'll just have to play at least several hundred times. Beginners tend to groan at that, and can get discouraged. When you commit to learning an instrument, you're signing up for a lifetime of repetition.
But I've come to like it. Repetition becomes something like prayer. Something gentle to keep your mind centered around something while the subconscious takes care of cleanup duty.
Or, for the secular, it's akin to the benefits of walking throughout the day. If you're not musically inclined, walking gets you pretty similar benefits. Just one foot in front of the other again and again. Connecting with something beautiful — in this case, nature.
For me, though, I like having a little tune learned by the time I make it home.