Any time the humidity is high (most of the year), your chances of seeing Mt. Fuji are slim. Between that and the air pollution, the mountain rarely shows it face.

On my last trip, which was in early November 2007, I went to the Tokyo Metropolitan Government Building's 45th floor observation deck, and I still couldn't see it. I've had the best luck in December and January.

Presumably the ryokan you are looking at is in either Hakone or the Five Lakes area. In that case, you'll have pleasant scenery with or without what my fellow foreign students used to call "the Fooj," and a lot of plants will be in bloom.

A high-end ryokan in a non-urban area is a memorable experience with or without Fuji.