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.
Day 5 and 6: Kyoto. No Japan trip is complete without visiting the ancient capital of Kyoto. There are many trains per hour between Kyoto and Tokyo and the journey takes about 2 hours and 20 minutes. We arrived in Kyoto around lunchtime and headed down to the Gion district.