The monkeys just roam around free; the whole hill is their territory. There's a visitor station where you can go inside and buy food to give to them through the chain-link fence covering the windows. And you can wander around outside and watch them. (But don't stare or point cameras at them too blatantly! That makes them grumpy.)
When we visited last time we were here (almost a decade ago!) we were in a rush to get up there before things closed at the end of the day; it's much more pleasant to do it in the morning when you can take your time.
After that we went back down the hill and went to an Owl/Cat Cafe! Well, forest. It had an area you could walk through with a bunch of trees and owls that you could say hello to and pet (gently, on the back, using the back of your hand)! They were very soft. And then it had a separate section with a bunch of bengal cats (domestic cats with jaguar-like fur coloring) you could hang out with. They weren't super-friendly kitties, though they were very interested in Jerry's backpack, which I'm sure smelled like our kitties at home, but we got to get some scritches in. Yay!
We had lunch at a nearby restaurant afterwards, then went a block to Tenryuji temple to see the gigantic heavenly dragon painted on the ceiling of the dharma hall. As we were leaving, an elderly lady asked if we were friends. "Good friends?" she asked, and we showed her our wedding rings, and she cheered and high-fived us. :)
That was a lot, so we decided we didn't need to see the main set of buildings (which needed a separate ticket), but we stopped by a little side temple that wasn't normally open to see a statue of Bishamonten, a patron god of martial arts; a very pretty "dry" garden (no pond) and a bunch of excellent paintings.
We got green tea ice cream on the way back to the train station and headed home. For dinner, after a second unsuccessful attempt to eat at a well-recommended okonomiyaki place, we ate at a tonkatsu place on the dining floor of the Yodobashi building.
To finish off the evening, we did karaoke! Which means a private booth with fancy lighting and a minimum order of one drink per person plus one food item. Kinda weird from an American perspective, but we had fun. And sang very badly.