The prefectural Budokan is in Fujieda, but I'm guessing that is a 2 hour train ride from where you are. Tokai University isn't too far from you so that may be an option. Here is a link to a directory of Judo schools in Shizuoka:
The fourth one is in Mishima and sixth is in Numazu which isn't too far from you. I'd guess less than an hour by train. If these are too far just stop by the local police station and ask them where the closest school is.