Photo: 663highland, CC BY 2.5 via Wikimedia Commons
It's across the river from Byōdō-in, near Ujigami Shrine and the Keihan Uji station. The latter third of the Japanese classic The Tale of Genji took place in Uji, and there are statues sprinkled throughout the city to commemorate that. It all reaches a crescendo at the Tale of Genji Museum. There are English audio guides available to use for a self-guided tour to help you better understand the exhibits, as well as the video. Those familiar with the story will probably appreciate the museum, and perhaps the city itself much better.
The Tale of Genji Museum is in Uji, Kyoto, Japan. It displays the world of the early 11th century Japanese classic novel The Tale of Genji with projected images, models, and exhibitions. The culture of the Imperial Court of the Heian period, the aristocrats' costumes, and the furnishings of their residences are shown.
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天ヶ瀬ダム
This dam is south of the city. A scenic walkway leads there from Uji either shore of the river and the dam itself offers nice views.
三室戸寺
One of the settings of the Tale of Genji, as well as the 10th temple along the Saigoku 33 Kannon Temple Pilgrimage Route. This temple will be of high interest to those who love flowers and gardens. Around the temple, lotus flowers have been planted in pots. Within the entire temple complex however, there are thousands of hydrangea, rhododendron, and azaleas all over the mountainside, and there are paths throughout the garden, so you can enjoy the flowers as you walk among them. The best time to see the flowers are from mid-May to July.
興聖寺
A Zen temple that features a long, justly-famous tree-covered approach from the river. It's a lovely walk in the autumn. Kosho-ji is a working temple, so while visitors can walk the grounds, the temple buildings themselves are frequently in use. Keep quiet while you're there; zen chants hang in the air in the late afternoon.
宇治上神社, ujigami-jinja
This modest little shrine is another one of Uji's historic monuments recognized as a World Heritage site. It's said to be the oldest Shinto shrine in Japan and was built to console the soul of Prince Uji no Wakiiratsuko, who committed suicide in the Uji River.
宇治神社, uji-jinja
The Uji shrine and the Ujigami shrine next door used to be part of the same complex, then known as Rikyukamisha. An interesting feature is the rabbit sculpture, which is said to have prevented the deity from getting lost.
対鳳庵
This tea house, operated by the town of Uji, is located along the river close to the Byodo-in temple. The tea ceremony is held in a traditional Japanese building with tatami and table seating. The tea on offer is either Sencha or Matcha, however you don't get to choose, it is whichever is on offer that day. You can buy tickets in the tourist information office right next to the tea house.