You should definitely not miss the Yutoku Inari Shrine - it is one of the jewels of Kyushu, yet unknown (and hence, uncrowded
) and far better than Kitakyushu.https://youtu.be/2UU_1Aip_l4
Since you'll be in the area around Xmas, take a look at the various illuminations they do for the holidays.https://matcha-jp.com/en/1474
For your Day 1, your places work if you are primarily interested in shopping (especially women's clothes).
Otherwise, not much going on there. You could visit other great places in the city though.http://www.thejapanfaq.com/fukpic.htmlhttp://bit.ly/1KAm8cU
For your Day 2, if you are seeing Shofukuji, you can also see Tochoji, next to the Gion subway station, with Japan's biggest wooden carved Great Buddha (and free
). The other big shrine dear to the people there is Kushida Shrine. For Ohori Park, be sure to stop by the nice traditional garden on the south end, and next to the park is Maizuru Park with the castle ruins. Plus 10 minutes north is Nishi Park, with some nice hills and places to walk through. They are both big cherry blossom spots, but you won't see that in December. Nanzoin which you have elsewhere is also a gorgeous place you should not miss.
For Nagasaki, you likely could fit in more than just Chinatown and Mt Inasa in a day. Don't miss trying the chanpon and saraudon for lunch or dinner. Otherwise, Chinatown is quite tiny and doesn't take long - but there are a number of other good spots.http://bit.ly/2ob4u8i
For Kumamoto, with the castle closed, the Suizenji Garden is one of the few other good places to see.http://bit.ly/2HopvoC
If you can make it over to see Aso, then it is a different story. It is best with a rental car, but it is a unique chance. The first big question is if you're willing to spend the money on a Northern Kyushu Rail Pass for it all, and the second is if the volcano cooperates and lets you go up to the crater. It's hit or miss.http://www.aso.ne.jp/~volcano/info/
Others have suggested Kitakyushu, but to me it's only really worth it if you combine it with some sightseeing in Shimonoseki. If the weather is good, there are some very good views from the Yume Tower, Hinoyama, and in Kitakyushu, the Mojiko Retro Observation deck. At night at Sarakurayama, you can get a killer city view that rivals the best in Japan.https://youtu.be/Hl1pCW9Ibbk