If you're going to stay in Kyoto, it's better to go to Nara, Osaka and Kobe, which aren't that far from Kyoto. They have so many spots to see that I can't write all of them here. As far as I know, Himeji Castle, which is designated as a World Heritage, is popular among tourists from foreign countries, too. Todaiji Temple and Horyuji Temple in Nara are also worth seeing.
And then, Miyajima in Hiroshima is famous for its sight. There you can see Itsukushima Shrine, which is also a World Heritage. Actually, Hiroshima is a little bid far from Kyoto and it costs you a lot, but you can buy a JR-free-pass if you come here as a tourist.