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Where would you suggest to visit in Japan other than Osaka that's not too touristy?

Good question, Kyoto and Nara are close but will touristy, Kobe less so. Getting away from the really famous cities would be best if you want to avoid tourists. Wakayama, Tottori, Shimane are pretty rural. Kyushu is nice too.
Depends a lot on what you want to do or see. :)