I second the suggestion to visit Hiroshima & Miyajima Island which is a short ferry ride from Hiroshima. Getting to Hiroshima is about 2 hours on the Shinkansen (bullet train) from Kyoto. If you don't want to go that far, consider at least doing a day trip to Himeji castle, one of the few original castles still standing and fascinating!
Kyoto and Osaka are very close to each other as well. I would take a couple of days from Osaka to visit Hiroshima or Himeji. You can also just be stationed in one place (either Kyoto or Osaka) and travel to the other as day trips so you don't need to move hotels. I would vote for staying in Kyoto and doing a day trip to Osaka. But you know best how you travel and your preferences.
Once we get closer to winter, visit a Dollar Store and get yourselves some gripper slipper socks. You will need to remove shoes for visiting temples and Himeji, and the floors are very slippery. I wouldn't want to be on my regular socks or barefoot. I brought a couple of slipper socks with grippers that I tossed at the end of the trip.