Tohoku Sendai Matsushima Hiraizumi Akita Kakunodate Nyuto Onsen Aomori Hirosaki Lake Towada Shimokita Hanto Dewa Sanzan Aizu
Kanto Tokyo Yokohama Kamakura Nikko Kinugawa Hakone Kawagoe Kusatsu Ikaho Minakami Narita
Chubu Nagoya Inuyama Mt.Fuji Fujigoko Izu Peninsula Nagano Matsumoto Kamikochi Kiso Valley Hakuba Yudanaka Sado Island Takayama Shirakawa-go Gujo Gero Onsen Kanazawa
Chugoku Hiroshima Miyajima Onomichi Okayama Kurashiki Matsue Iwami Ginzan Iwakuni Yamaguchi Hagi
Shikoku Takamatsu Kotohira Naoshima Matsuyama Uchiko Kochi Tokushima Naruto
Kyushu Fukuoka Dazaifu Nagasaki Kumamoto Mount Aso Minamata Beppu Miyazaki Takachiho Kagoshima Kirishima Yakushima
Okinawa Honto Miyako Yaeyama
Even medium-sized stations have luggage lockers, so you will definitely have no problem at any of the major stations you list.
Small size lockers typically cost 300 yen, but it can vary.
How big is the locker?
See this page for average sizes:
http://www.japan-guide.com/e/e2274.html
Do traveller required to bring their own lock?
No.