Japan National Tourist Orginization’s List in Japan (PDF file) lists camping grounds in the most well known tourist areas such as Nikko, Karuizawa, Hakone, Okutama, Kamikochi, Nagiso, Sado Is., Kawaguchi-ko, Takayama, Kawayu, Himeji, and Miyajima. It gives you an idea of the wide variety of services, prices, and open-seasons. Being a JNTO listing, they tend to be more reputable and less run-down than you might find via a Google search of Camping Places
Will Ferguson’s “The Hitchhiker’s Guide to Japan“ (Chas. Tutle, 1998, ISBN #0804820686) is a very good resource for anyone planning to travel on a budget, or go camping or hitch-hiking in Japan. It is half cheap travel tips and half route and destination information for Hokkaido, Tohoku, Shikoku, and Kyushu. It may be somewhat dated though.