I have shared a day trip sample itinerary of Fuji and Hakone before.
But this itinerary covers both Lake Kawaguchi and Hakone areas in one day. It is very tight and many places are not covered. If you can spend two days, you can enjoy Fuji and Hakone areas one day each. You can visit many more places easily.
In this sample itinerary, I tried to put most of popular spots in these areas. And also this plan includes Fuji Shibazakura festival which is most popular event in spring. You can do this trip from Tokyo to Tokyo. You also can squeeze this trip between Tokyo and Osaka. You can drop by this area on the way to Osaka or Kyoto from Tokyo or versa.
This itinerary has been created by timetable in March, 2018. If you try to do this plan, please check the updated timetable before you go. Continue reading