Typhoons, including the ones in the past few weeks, rarely make it as high up north as Tokyo (which, for what it's worth, is also on the coast) so this is no reason to avoid Kamakura.

While I like Yokohama, I don't think it's all that much different from Tokyo, and either Kamakura or Nikko would make a better 'escape' from the city. Nikko in particular, being quite far away, is set in a lush forest that should be turning beautiful autumn colors pretty soon now, esp. if you escape the planted evergreen cedars of the shrines and head to Lake Chuzenji.

Some recommendations for both, mostly written by yours truly:
http://wikitravel.org/en/article/Kamakura
http://wikitravel.org/en/article/Nikko