Is Setouchi Aonagi a resort near Matsuyama in Shikoku? I can't speak to that resort, but there's lots to see in the wider area. Matsuyama itself doesn't have the historic charm of Kanazawa or Takayama, but it's a fun city with some good dining. Most people in Matsuyama visit Dogo Onsen, where the major attraction is a historic onsen bath house (currently undergoing restoration). It would be worth checking if there are onsen hotels in the area that allow tattoos. Matsuyama also has several historic temples that are on the 88 temple pilgrimage route. Just to the south of Matsuyama is Tobe, a pottery town. Also to the south of Matsuyama are a couple of towns with cute historic quarters - Uchiko and Ozu. In Ozu, there's an upscale hotel (Nipponia) in the historic area, which also offers accommodation in the castle. Further along the railway line on the coast is Uwajima, another castle town with some regional dishes that are worth trying, including "Tai-meshi." (Sea-bream sashimi rice bowl).

You can take a ferry from Shikoku to Oita prefecture in Kyushu. You could do that if you're planning to visit Fukuoka. There are a lot of nice onsen resorts in Oita. I can't tell you much about that area, but it's getting less difficult in general to find places that welcome tattoos.

Some other historic towns in Western Japan include Kure and Onomichi in Hiroshima prefecture. Hagi, on the Japan sea coast of Yamaguchi prefecture. and Matsue in Shimane Prefecture (also on the Japan sea coast). They're mostly small towns. Matsue is a small-to-medium-sized city (about 200,000 people).