So Godot tells me Jeri shared neat new site that shows you on a map where Pokemon are and how long they've got left to be there. I'm gonna go try it out later after my phone recharges, but have a look: https://pokevision.com/
That being said, I took over 5 gyms and found 2 friendly ones with slots open. So grand total of 70 coins, 3500 stardust, and a 21 hour cooldown.
So confirmed, if you have one gym, cooldown is 20 hours and any more than that the cd is 21 hrs.
If my luck keeps up, I can save up for some free incubators or lucky eggs. Thanks to all the stops on campus, I will never run out of pokeballs.