The thing about visiting shrines in Japan is that they're everywhere and they're all special in their own way. So explore the ones in whatever neighborhood you're staying—they're bound to be peaceful and interesting.
If you find yourself in Tokyo's Minato neighborhood, climb almost 30 yards up the steep stone steps to the Atago Shrine. The story goes that a young samurai rode his horse up these stairs to deliver a plum blossom branch to the shogun.
Today the stairs are a symbol of individual success, and recent college graduates apparently climb them before job interviews.