I think walking is on the right track. If you feel mental fatigue from playing music (or other hobby), you will need to recharge and get new inspiration.
Physical activity is the best way to let the mind recharge.
Personally I currently have a lot of wood to chop, and so I do that hard manual labor just to disconnect the mind. People keep asking me if I want to borrow their electric wood chopper. I have turned down 5 people by now, and my in-law even delivered one without asking - insisting to help out. Obviously I don't use it, because that's not the point at all. If I wanted chopped wood I could simply buy it. I want to chop wood, because it's a way for me to mentally zone out.
Anyway, you can spice up your walks by bringing a sketch pad and draw something. Perhaps that'll keep your mind more focused on observing the sorroundings and giving a purpose to the walking.