Mikami Shrine is a holy place where religious souls meet to pray. You can do the same, or simply observe others in worship.
You'll have no end of sightseeing choices when staying in Arashiyama. Mikami Shrine is an ideal place to kick off here, but there are numerous other fine sights to discover. Nijō Castle, Kyoto Imperial Palace, and Kyoto Tower are near the sacred place and and will cap off your day nicely.