Fitness is just as common in Japan as Australia. Central, Fitness First and Konami are some of the big fitness gyms here.
I have lived in rural Japan before, and you will be hard pressed to find a big gym. At best, you may find a small gym attached to someone's house who sells membership to the locals. Probably the size of around 20 tatami mats and just basic weights. You will probably have more fun going for morning runs and buying your own dumbells etc.
Going on a working holiday visa shouldn't really close doors for you. Actually, many schools will like this fact as they don't need to stuff around with your visa. Especially so the smaller rural schools! I suggest searching online for the schools. Something along the lines of "english school wakayama" or "英会話wakayama".
英会話 = English School
和歌山 = Wakayama
静岡 = Shizuoka
Another area you may consider is Mishima or Numazu which is located right above Isu Hanto. Try "Merry House English School". I used to work for them many years ago and am sure you will love the area. It's not too far from the coast and plenty of rice fields and am sure there is a big gym nearby. The website used to be
www.merryhouse.jp/ but seems down at the moment.
If you come across an English school only in Japanese, don't hesitate and still contact them.
Good luck with the search.