It's now New Year's, but I take you are talking about the end of 2018, right?
It would help if you gave more info like how many days your trip will be, as well as your interests.
All the places you mention have some great places. And while travel during New Year's can be a headache, it's also an opportunity - experience the New Year Japanese style.
Getting to the Sea of Japan(Tottori, Matsue, Izumo, Hagi) and travel around is very time consuming. If you have to get rid of something due to time, I'd say leave that for a future trip. Next time fly into Tokyo and just catch a flight to near there to start off. For this trip, don't go too far from the bullet train line.
Bunny Island is also rather time consuming, but there are not a lot of places to go where you can get mobbed by rabbits. Definitely something you won't forget. But it may eat up at least half a day just for one place.
Akiyoshido is the ideal place to visit regardless of the season or the weather. Inside is a constant temperature, though pretty humid. The experience though is surreal.
https://youtu.be/DqIKC9S8TFQTsuwano & Iwakuni are also very good - Taikodani has a good Inari feel without the mobs that are at Fushimi Inari in Kyoto.
http://bit.ly/2CgIvaRBoth Onomichi and Kosanji on Ikuchijima are excellent.
http://bit.ly/2wL4cfNYou might consider adding Miyajima too.
Plus Fukuoka, Nagasaki, Kagoshima, and Beppu all have some good sights.
http://www.thejapanfaq.com/fukpic.htmlThe question is, do you have the time for all these places. Only you know your travel interests and pace.