Shintoism, non-Buddhist ethnic religious practices in Japan, is one of the many things that never changed in the modern Japanese society: you can find Jinja (shintoism shrine) in any towns or cities. Every Jinja has there own Kami (god), and the Sapporo Jinja was built to serve the god of Hokkaido.
During the Sapporo Matsuri (札幌まつり: Sapporo Festival) in mid June, is the biggest festivity among all year around.
Entrance to Jinjas are free, but you should keep quiet and respect the atmosphere.
北海道神宮: Sapporo Jinja
dyii added
Visit http://en.wikipedia.org/wiki/Shintoism to get information about Shintoism. It may give you some ideas before visiting the Jinjas. :D
