The city of Kamakura rose when the clan lord Yoritomo defeated another clan's warlord (whose son was earmarked to be emperor) and became number one in Nippon as 'shōgun,' though some doubt his control over the Kansai region. He moved to Kamakura in 1180. Hōjō clan lords took unofficial power by 1204 by Kamakura remained central.
Source for history: Wikipedia article on Kamakura, accessed March 4, 2017, although some of the material was already known to me from books I've read.