Although two major non-JR group railway companies operate in Kyoto, Hankyu and Keihan do not operate to Kyoto station. Therefore most of the foreign tourists do not use these railway companies during their stay in Kyoto or even in Kansai region including Osaka and Kobe.
On the other hand, Kintetsu, another major non-JR railway company in Kansai region has its terminal at Kyoto station. The difference between Hankyu/Keihan and Kintetsu is that Hankyu and Keihan are connecting Kyoto and Osaka. Although Kintetsu operates in Osaka, it does not have direct trains connecting Kyoto and Osaka. On the other hand, Kintetsu has tracks running toward to Nara.
Japan Rail Pass holders dominantly use JR Nara line to travel between Kyoto and Nara stations but actually traveling by Kintetsu between these two cities are faster and cheaper than JR trains. Then, Kintetsu Nara station which is not annex to JR Nara station is much closer to Todaiji temple and Nara park.
Also there are direct limited express trains running between Kyoto and Ujiyamada station in Ise, Mie prefecture. Ujiyamada is the gateway to Ise jingu shrine.