Kyoto is the home of Pure Land Buddhism (Jodo Shinshu) founded in the early thirteenth century, and the temple was built in the mid-1500s.
A half-century later, Hongwan-ji had accumulated enough power to threaten this cat named Tokugawa Ieyasu, who cleverly encouraged a breakaway faction to set up their own hongwan-ji a little distance away. About a ten minute stroll for a middle aged fat guy. The old temple became known as Nishi (West) Hongwan-ji, and the new, larger, more impressive one, as the Higashi, or East, Hongwan-ji. The "new" one of say, 1602, is one of the world's largest wooden structures, but it's being refurbished underneath an even larger aluminum-sheeting structure, which is surely not in the running for largest.
Incidentally, you don't drink the water from the dragon's mouth trough, you wash your hands, then scoop some water into your palm which you use to rinse your mouth, and spit the water onto the surrounding gravel. All the Japanese Buddhist temples I went to (only four, I'll grant you) had this.
Kyoto's most famous place of worship is a Shinto shrine, world-reknown for its endless path of massive orange torii. The entire circuit is about 4 km, uphill both ways. It's only three stops south of the Station via subway or train.