I will offer a few thoughts:
1. The first time I visited Japan I only went to Tokyo, from January 2-4. I didn't like it, I thought it was cold and dreary and it seemed like almost everything was closed. Things in Japan will be closed on January 1-3 they way things in the USA are closed on December 25 or January 1. On the other hand, shrines and temples in Kyoto may be quite crowded on these days, I don't know.
2. I really like Nagasaki, there are interesting historical sights there a pleasant waterfront and area with old European buildings. As it's in the south of Japan, it may be warmer this time of year. There are direct flights from Okinawa to Fukuoka and then it's a 2 hour train ride to Nagasaki. Then you can fly from Nagasaki airport to Osaka or Tokyo I think.
3. I went to Okinawa this year. I didn't really like it. You pretty much need to rent a car to get around, I couldn't get used to driving on the "wrong" side of the road. The Himeyuri monument/museum was probably the highlight. The underground naval headquarters and peace park are also good. You can also visit "Hacksaw Ridge" but there's not much there.