Japan is great in any season - it really depens what you're looking for!
the coldest months
Around Tokyo it rarely drops below 4C. January is a very slow season, so you will encounter very few tourists. Beware that the turn of the New Year is generally a quiet time and not celebrated as loudly and lavishly like other parts of the world. By the end of January, southern parts of Japan may be starting to feel spring-like, while it's peak ski season in Nagano and Hokkaido.
the most expensive season
With cherry blossom season fast approaching from the middle of March, Tokyo and Kyoto in particular become a lot more busy, culminating in the first week of April, when the blossoms are usually in full bloom and flights as well as hotels are at their most expensive. If you want to see the cherry blossoms outside of the crowds I highly recommend to explore more rural places like Shikoku (see my itinerary!) or Tohoku.
Golden Week + start of summer
Depending on the year, it can already get as hot as 30-40C degrees from the beginning of May. No matter what you do, avoid the Golden Week in the beginning of May at ALL(!) costs. It’s the one holiday week where it is crowded absolutely everywhere you go as most Japanese use the prolonged holiday to travel within Japan. From the middle of June, rainy season slowly starts but blesses many places with an abundance of hydrangeas.
Rain + typhoon season
It gets very hot and humid; the worst time to visit Tokyo and Japan in general. Flights get canceled and delayed if a typhoon approaches and temperature easily get as high as 45C. If you want to climb Mt. Fuji though, these are the only months you are able to do so until about the middle of September. If you do want to visit in summer, I highly recommend to spend time in more mountainous areas such as Nagano or Yamagata, enjoy the tropical islands of Okinawa or go to the beach around Kamakura. Tokyo is definitely the least fun as the city heats up significantly during summer.
One of the best season to visit Japan
October of the best seasons to visit! I would avoid most of the first half of September as typhoons are still frequent. In the latter half, the weather is still summery warm but not hot anymore. Crowds are little after the summer vacation time and you get to enjoy many sights without the crowds. Halloween is a big event, so if that is your jam, I highly suggest a visit at the end of October. Depending on the weather, very little places will have fall foliage already in October unless you travel to the colder regions of Hokkaido, Tohoku or Nagano where the peak falls usually around the end of October.
Fall foliage and Christmas decorations
The most seasoned travelers will go to Japan in November. It is the cool, crisp and dry time of year. Fall foliage peaks only near the end of November, some years even in December for Tokyo especially. Also, Tokyo has amazing light shows for Christmas and I enjoyed Tokyo in December more than NYC!
Go check out my guide for the best free things to do as well as itineraries and travel tips to make your trip unforgettable.