[QUOTE
Travelling in June, I'm a bit concerned about the rainy season, especially doing a lot of walking and public transport./
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I was in Japan in June last year. A tsunami was coming in from the S.E. So I switched up my plans to give some distance from it till it passed - took a bullet train. Even the couple days of a bit of rain/humidity did not do anything to dampen my spirits. And I took public transport and walked alot. You can be anywhere in Japan and enjoy the culture and the food. I was amazed at the number of people that had a of grasp of English. English is taught at an early age in Japan.
Btw, I am going back this May/June for 1 Month.