A very well-thought-out itinerary. How I envy you for having so much time and money for a 1-month trip.
I presume you do not want to change hotels too often, as you are travelling to and from Osaka a lot. There is nothing wrong, but just want to point out that Kurashiki and Kobe are en-route from Hiroshima to Osaka.
In Kyoto, I will add Ryoan-ji, Heian-jingu, the Philosopher Walk and the ever popular Gion district.
In Takayama, when you say to go to the Hida Fold Archeological museum, do you mean the Hida-no-Sato folk village!? If it is, I would skip it since you are going to Shirakawa-go. There is no need to go to the folk village to see the reconstructed gassho-zukuri farmhouses, there are plenty authentic ones in Shirakawa-go.
As for Mt. Fuji, I agree there is not much point of going there if not climbing it which you cannot do in winter. To see it in its glory for afar is better, though it is not easy as it is mostly hidden behind clouds. You may have a chance of seeing it with Lake Ashi as fore-ground in Hakone. Speaking of Hakone, I would strongly suggest to spend 2 days there to take in all the sights and have an overnight stay in an onsen ryokan. The Hakone Free Pass is good for 2 days anyway.
Nikko with Chuzenji-ko and Kegon Falls can be packed in a day-trip from Tokyo if you start early in the morning. Take the bus to Chuzenji-ko first upon arrival. There is less crowd and less traffic in the morning. Come back in the afternoon to do Nikko, you cannot escape the crowd in Tosho-gu anyway. Also that way you will be walking downhill back to the rail station instead of up. Be warned that Chuzenji-ko area is much colder in winter.
As for Kawagoe, it is an easy side-trip from Tokyo, just need a few hours to take it the Candy Alley, Toki-no-Kane bell tower, Kita-in temple and the Kurazukuri merchant houses along Chuo-dori. If you go early in the morning, you can be back to Tokyo for lunch.
Though Sendai can be done as a daytrip from Tokyo, but it really deserves at least a couple of days. From Sendai, you can do at least half a day to Matsushima and half a day to Yama-dera. I see that you are going for the Manga Museum in Kyoto, so I presume you are an Anime and cartoon fan. Not far from Sendai in the town of Ishinomaki (further on from Matsushima) is Mangattan Museum. Actually the streets from JR Ishinomaki station to the museum are already lined with sculptures of cartoon characters and there is even a special train from Sendai which is decorated inside-out with cartoon characters.
http://www.man-bow.com/manga/