Nikko is another "escape to the mountains" day trip from Tokyo, and if you have a JR Pass, you can even go to Nagano for the day.

Actually, the (literally) coolest escape from the heat I ever accomplished was taking the bus from Takayama to Matsumoto over the Japan Alps. The rest stop was at Norikura-dake, which is above the timberline. Unfortunately, the brief respite made the heat in the lowlands feel even worse.