Kyoto and Nara are a short trip in either direction; most visitors will have arrived from one or the other.
Otsu If you are hungry for more Tale of Genji locations, visit Ishiyama-dera temple, where the book was written.
Ise is only a couple hours away; it's home to the eponymous Ise Shrine, possibly the holiest and most important Shinto site.
Osaka isn't far away if all of this classical atmosphere has you thirsting for a healthy dose of noise, neon and ferroconcrete.