When my mind is on idle I tend to go into anxiety cycles, which is bad. As such I've got into the habit of carrying my smartphone and headphones with me at all times, and playing podcasts and audiobooks continuously, often at double speed. I also have a mental calming exercise where I go through the integers in order and work out their prime factors (or if they are prime) in my head.

For me, having nothing to do is a luxury. When I find myself in this mode, I take long walks, let my mind drift and think about whatever it feels like (usually it chooses to think about one of my ongoing projects, big unsolvable world-scale problems, future, lack of moral progress, or sex), read long-form stuff (mostly Kindle books on my phone) and generally relax and recharge, assuming that I can find a relatively quiet environment.