LapLap

I've not been in that many typhoons but the first was a biggie - was at the start of October 2002, typhoon Higos http://en.m.wikipedia.org/wiki/Typhoon_Higos_(2002)
Same typhoon that interfered with filming of Lost In Translation. Wind was severe, rain was horizontal, luckily the worst of it in Tokyo coincided with my visit to a large exhibition centre in Makuhari Messe, couldn't have been that bad, found myself just a few metres from Prince Naruhito and made a couple of businessmen giggle when I asked who he was, his safety was obviously not in question. By the time I got out much of the wind had subsided. Hardly any bicycles were left standing.
Next day was the day I met MrLapLap and we went to Hakone. We did the Hakone circuit as soon as we arrived in order to take advantage of the clear skies and beautiful weather, just in time as Fuji San hid behind a shroud of mist for the remainder of our stay.
It is very unlikely that a typhoon as powerful as this one affects your trip. Unlikely, but not impossible. None of my flights were affected, none of my travel plans needed to be rearranged.

yyznomad

Made one of the last shinkensen trains out of Shin Osaka to Tokyo yesterday. This morning at 7am post-Typhoon, opened up my Westin hotel drapes to see clear blue sky and a perfect unfettered view of Fuji san. Rare for me considering it is my 15th time here and it is always blocked by cloud or Tokyo smog.

hamnori

Japanese has a specific term for that - a clear sky after the smog has been blown away by the Typhoon - Taifu Ikka(台風一過)