A typical schedule for climbing Mount Fuji is to:

• take a bus to the 5th station,
• stay at the 5th station for a couple hours to accustom yourself to the altitude,
• start ascending at evening/night,
• optionally sleep (take a nap) at a mountain hut,
• arrive at the summit before sunrise,
• see the sunrise and take a rest for a while,
• start descending
• arrive at the 5th station, and
• take a bus.

If you are coming from foreign countries (or somewhere in Japan far away from Tokyo), you may also want to visit Tokyo for sight-seeing.
In this case, the most convenient access from Tokyo to Mount Fuji is a highway bus.
http://www.japantravelinfo.com/features/features_item.php?featuresid=40
This highway bus takes you from Shinjuku station to the 5th station of Kawaguchiko Trail (or vice versa) directly.

Shinjuku Highway Bus Terminal is located at the outside of the West Exit of Shinjuku station.
The following map shows the location of the bus terminal and 3 reasonable hotels nearby.

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