Seriously? This is gonna be a long list ..... I try to go with the not so standard tourist spots, I guess.
My problem is that I've been to almost everywhere in Japan .... and there were so many great places that it's hard to pick just a few ...
Mt. Osore in Aomori Prefecture (one of the 3 most sacred places in Japan next to Mt. Hiei and Mt. Koya)
Amanohashidate (one of the top 3 views of Japan besides Miyajima and Matsushima)
Tashirojima (also known as "Cat Island" in Miyagi Prefecture)
Mt. Unzen in Shimabara (they burned Christians in the hells of Unzen a long time ago ..)
Gunkanjima in Nagasaki (Batttleship Island - Ghost Island!)
Akiyoshidai and
Akiyoshido in Yamaguchi Prefecture (one of the biggest limestone caves in Asia)
Nartuo whirlpools in Tokushima Prefecture
Tottori sand dunes (ride on a camel and forget that you're in Japan!)
Kotohira / Konpirasan (walk millions of stone steps up and enjoy a great view)
Hirosaki Castle during cherry blossom season in Aomori (enjoy a cherry blossom moat)
View from Mt.
Hakodate in
Hokkaido (said to be one of the best night views in the world)
Nokogiriyama in Chiba Prefecture (has the biggest Buddha statue outside)
Mt.
Yoshino in Nara Prefecture during cherry blossom season (most famous spot for cherry blossom viewing in the Kansai area)
Shirakawa-go (any season) (you won't believe you're in Japan!)
Uhm ... I could go on forever, seriously!