Osaka has a really amazing looking castle. Unfortunately once you go inside the castle you realized that it's actually a modern steel and concrete building made to look like the original Osaka Castle. The inside if the castle is a museum and looks nothing like what the castle actually looked like on the inside, there's even elevators and escalators.
On one of the mountains surrounding Kyoto is the Iwatayama Monkey Park. It's a pretty interesting area at the top of a small mountain where about 170 Japanese Macaque live. It's about a 20 minute walk up a fairly steep trail to get to the top of the mountain where the monkeys are wild and free to roam around.
One of the really interesting things about Nara is that there's hundreds of small deer that roam the city freely. The deer are thought to be heavenly animals that protect the city and the country.
Vendors sell deer cookies that you can buy to feed the deer. You have to be a little careful when feeding the deer because if a group of deer sees that you have the deer cookies, you'll quickly be surrounded by a huge pack of deer. I saw several times where little old ladies would start feeding one or two deer, but then they would freak out when they became surrounded by twenty or thirty deer.