It’s more when I want to visit a gym or when I have a Quest with ‘Battle in Gym …’ to me.
Other: early evening, so generally between 7 and 10 PM. Simply because 7 PM is “rotation time” here. Depending on what shift I work, I might be a bit later (but still before midnight, so people of the previous days’ team at least get their coins), or check back again sometime early morning (in case spoofers took over during the night, so I can recap my own gyms and at least kick them out of other teams’ gyms and place a Weedle or somethinig like that.
I hit some my gold gym badges on my way to work. Then I hit some of them on my way home. On my days off, I hit different ones while dropping my kids off at school. I only do the gym that is about to host the Legendary Raid if my team already took it. Otherwise I let the team who owns it, keep it. I can only see 1 Gym from my house and it kind of bothers me when another team is in it. So yeah, I fight that one a lot.