Is it more advisable to stay in the Mt. Fuji area or travel from Tokyo?

(Kansas, USA)

For a once in a lifetime trip (early September), I hope to spend a week in Tokyo and almost a week hiking and bicycling in the Mt. Fuji area, including going to the Mt. Fuji summit.

Given the need for making travel reservations far in advance of weather forecasts, I wonder whether it is more advisable, to maximize chances of good climbing weather, to arrange a stay in Tokyo and 'commute' to the Mt. Fuji area in spells of dry weather or make reservations for a week in the Mt. Fuji area and hope for the best?

So many variables, so few crystal balls ;) but would appreciate the voice of experience. Many thanks for your terrific site and the opportunity to ask a question.