I spent a month in Japan last year, we spent several nights in Tokyo exploring, then Fuji Five Lakes, the Japan Alps, then Kyoto, Hiroshima, Fukuoka, Yufuin.
My thoughts:
Fuji Five Lakes - great views of Fuji, weather permitting. A couple of hours from Tokyo so could be a one or two night trip.
Japan Alps were amazing and very beautiful. My faviourite part of the trip, we had a week in the Alps. With your spare days in your itinerary I’d consider putting the Japan Alps in.
Kyoto - this was my least favourite -only because everywhere was extremely busy. Be prepared, some of the temples, shrines and major sites are absolutely rammed. There was a lot to see - so I do think it’s worth it - but personally I wouldn’t go back on my next trip. I’d rather spend more time in the mountains or on the islands. The day trip to Nara was definitely worth it as was Fushima Inari.
Hiroshima - very interesting and a vibrant city. Miyajima is amazing and worth spending at least a day if not overnight.
Fukuoka - we used as a base to explore Kyushu and to travel to Yufuin which I loved. There are some beach destinations on Kyushu if you wanted a few days on the beach - and you wouldn’t have to fly. We didn’t make it to Okinawa but these islands would be another possibility for the days you haven’t planned yet. You’d have to fly but it’s not that expensive/not a long journey.
Anyway I am sure you will love Japan it is amazing.