Surely one of Tokyo's most visited sites is the home of the Japanese emperor and his family, the Imperial Palace, located several minutes walk from Tokyo Station. Parts of the royal compound are opened to the public for guided tours and the official website has a link to the application forms necessary to join an imperial tour. You're unlikely to see any of the family themselves but it does provide a glimpse into their lives. http://sankan.kunaicho.go.jp/english/guide/koukyo.html
Photo: Big Ben in Japan