This Shingon-sect temple, founded in the 8th century, has a lot going for it, including Japan's oldest pagoda (the Tah艒t艒, built in 1194) and an impressive location atop a stone outcrop, but it's most famous for hosting one of the world's earliest artists-in-residence: according to lore it was during a stay here that Murasaki Shikibu first dreamt up The Tale of Genji, in 1004.
There are also lovely walks through the grounds, partly forested and partly manicured, and views of Biwa-ko from the pavilion Tsukimi-tei. The temple is a 10-minute walk from Keihan Ishiyama-dera Station (continue along the road in the direction that the train was travelling).