First Triumvirate Triumvir or tresvir: member of a college of three members. The expression is mostly used to describe the First Triumvirate (60 BCE; Pompey the Great, Crassus, and Julius Caesar) and Second Triumvirate (43 BCE; Marc Antony, Lepidus, and Octavian).
With 8 nights, I suggest you spend 3-4 in Tokyo, 1 in Hakone for ryokan, 3-4 in Kyoto. Hakone offers Mt. Fuji views on a clear day, and it sits right off the train line between Tokyo and Kyoto so it's an easy detour. While at Kyoto, spend a day at Nara.
Best Tokyo Airfare OptionsPrior to purchasing tickets to Tokyo, you should decide where your priorities lie. Depending on your originating airport, you may be able to find Tokyo flights with only one stop that are a minimum of 15 hours in length.