The one thing that really sticks out is your plan for going back to Tokyo from Nagasaki in one shot. I hope to God you are planning to fly - if you used a rail pass it would take you over 8½ hours and with the faster Nozomi train, about 7 hours. Either way, it's completely murdering the day. You could take a low cost carrier like Jet Star for at little as 4500 yen to Narita, or there is ANA's Experience Japan Fare for 10,800 yen to Haneda.
http://www.jetstar.com/jp/en/homehttp://ana.ms/20Xtf8tFor your arrival day, you may not be crossing a lot of time zones, but I wouldn't expect too much on your first day - you will still likely arrive dead tired and not ready to start storming the tourist sights. And regarding your plans in Tokyo, you should definitely check where you plan to go carefully - many places will be closed at the end/start of the year. Typically shrines and temples are open, so go see those when other places are closed.
There is also little need to spend 3 days in Osaka if you are already seeing Tokyo. Everywhere has something of course, but Osaka really comes alive at night and you can easily go see the city after a day of sightseeing in Kyoto. For your daytime hours, you could certainly go and see Himeji for a day. The castle is the finest original surviving castle in the country, and the Kokoen Garden near it is exquisite.
https://goo.gl/65ZtRiGet the combo ticket for both and one is virtually free. You could also spend a day in Kobe if you like, and in Shiga, there is also Hikone Castle which is also a very nice original.
https://youtu.be/dCp5HCc6rYQOn Jan 11-12, you don't give times of travel, but I hope you give both Hiroshima & Miyajima the time they deserve. In Hiroshima City, there are so many people who just see the Peace Park/Museum and then leave. There is so much more to the city than that - the Shukkeien Garden is really nice, and the secret gem of the city is the Mitakidera Temple, which is as breathtaking as it is uncrowded.
https://goo.gl/fAz4axFor Jan 15, you might consider going to Narita early and seeing some sights there.
https://www.japan-guide.com/e/e6400.htmlIf you want a cheap way from/to Narita, there is the 1000 yen bus.
http://accessnarita.jp/en/home/