I just returned from a 2 month adventure backpacking around Japan. It was very different from the usual golden route, although I did go to those cities for a bit. Here are a few thoughts if you want a different experience compared to most:
My days were losely planned and chill. I booked a month of hotels and then booked the rest whilst I was there to allow flexibility. I would recommend this, as for the most part, you can still get good and cheap hotels even booking just a few days before. Especially in the latter half of the trip, I didn't plan much and researched good places to visit whilst travelling between areas. Highly recommend.
I used an Osprey 40l to carry everything. It's incredibly nice just having a carry on for a plane. It's also extremely convenient travelling around a country whilst carrying as little as possible. I had 6 days of clothes and toiletries. It's all you need. At the end you can buy a suitcase and gifts if you want. This is my biggest recommendation. Japan has more than ample resources to wash clothes and sustain you indefinitely. Don't bring a suitcase.
If you have been before or want something a bit different, I recommend Kyushu. It was my favourite area by far. The food was amazing and the people are more friendly. Places like Fukouka or Kagoshima had extremely few Western tourists and I just don't understand why. They're incredible places to visit.
Don't pre book shinkansen tickets. They're incredibly frequent and always have spaces. To keep yourself flexible, I recommend arriving at the station at your leisure. Then buying the next shinkansen on the Smart ex website. Pre connect your IC card and use it for shinkansens too.
I can talk about it forever so if you have any questions and are considering a trip like this then I can answer questions