The Ujigami Shrine (built in the 11th century) is adjacent to the Uji Shrine and is dedicated to the Emperor Ōjin and his sons, imperial princes Uji no Wakiiratsuko and Emperor Nintoku. It was registered as a UNESCO World Heritage Site as one of the "Historic Monuments of Ancient Kyoto."
The shrine also contains the Kiriharasui spring at the entrance, which was once one of the 'Seven Famous Springs of Uji'. It is said that the guardian spirit of the shrine is the mikaeri usagi, or ‘turning rabbit’, who once guided Prince Wakiiratsuko back to his home.
You can also get yourself a fortunetelling in the form of small ceramic rabbits - pay 300JPY, choose one rabbit from a box, and pull a string from it to know your fortune.
A small and beautiful shrine, but if you do not have a lot of spare time, I would recommend to skip it.