Ditto Kinosaki; it's a great onsen and is well worth the trip. You could do a two day trip there. I suggest going from Kyoto to Himeji in the morning; visit the castle, Kokoen, and Mt. Shosha (the latter can have surprisingly few tourists). In the early afternoon head to Kinosaki; the train ride is pretty nice. Try to arrive in Kinosaki around 5 pm. Get a decent ryokan if you can; visit the shops and a couple of the onsen, then eat dinner. Then relax by visiting some more onsen. Do more onsen in the morning, visit the temple, you can hike or take a cable car up the mountain, boil an egg in onsen water, and then head back to Kyoto.
Another option is Wakayama. Despite being relatively close to Kyoto/Osaka, there will be many places where you'll be the only foreigner. You could do a trip to Mt. Koya, Shirahama, Nachi Falls, Kumano, and on around to Ise.