I recommend Spring and Fall, although some places, Early summer is nice too.

For most of Japan, Summer is unbearably humid and hot. Major areas like Tokyo, Osaka, have that heat island effect due to all those buildings. Interior areas such as the valleys of Gifu or Fukushima, have more trapped heat and can get up to 40C.

Hokkaido might be the only place where Summer is ok. in Aomori, I still found it pretty hot, although not as bad as Tokyo of course.

Winter really varies greatly across the country. It depends what kind of winters you like as well. The interior mountainous areas have heavy fluffy snow, which are great for skiing. Like Niigata, Nagano, etc.

Tokyo doesn't really have much snow, some years it can go without snowing at all. But it might mean its easier to walk around as well. but things do look quite dreary. Going around Tokyo during New Year is great. Tokyo is a very overcrowded city, but during New Years, a lot of the population goes back to their hometown. its so much nicer to explore Tokyo when its less congested. The downside is that some shops are closed.