Pottery is a very traditional occupation and also a culture. There are many pottery classes held throughout Japan. If you are going to reside in Japan for a certain period, joining the pottery class is an ideal opportunity for you.
There are plenty of famous kilns in Japan, mostly are west of Tokyo. Six ancient kilns are Bizen, Echizen, Seto, Shigaraki, Tamba and Tokononame wares. All of them are west of Tokyo and none of them are neither in Kyushu nor in Shikoku. It is interesting that two notable wares in Japan, Karatsu and Arita are not included in these kilns. On the other hand, there are two kilns in Aichi prefecture.
Anyway there are many kilns and potteries made by the kilns are different. Therefore if you are in Japan for a short visit, please try to check and compare each pottery.