The two best things I did for my mental health was leave Facebook (years ago) and stop watching the news. Hacker News is my news source (along with Ars Technica), I don't look at anything more political or world-eventy than these two sources, and I am selective about links even here. I can't even stomach NPR anymore.
More recently on the mental health front, I've been drawing more. I'm not great at it, but it is relaxing and distracting.
Also ambient or jazz--opinion-free, story-free music.
So I am still feeling burnt out, but it is a slower burn.