If you're looking for worthwhile places to visit that are less known to mainstream tourists, I think that the San-in coast between Yamaguchi and Kyoto prefecture, is hard to beat. Hagi (Samurai town), Iwami Ginzan (Old silver mine town), Izumo Taisha (one of Shinto's most important shrines), Matsue castle and the gardens of the Adachi Museum of Art, The sand dunes of Tottori, Kinosaki onsen, the Tango peninsula with its famous sandbar that everyone photographs upside-down.

I think Wakayama and Mie have more A-List sites to offer (Koya-san, Ise Jingu, Nachi Taisha, Kumano Taisha, Kumano pilgrimage trails etc.), but they're far from secret gems - I would go so far as to say that some are very much on the "standard itinerary" for domestic tourists ... maybe one rung below the "standard itinerary" for tourists from abroad.

Being a pedantic asshat, I must point out that most of the San-in coast lies further north than Nagoya, but since the definition of "Honshu" has been stretched to include Shikoku, it's all game.

Shikoku is also worth a visit and much of it is off the beaten path. The cities of Takamatsu and Kochi are fun. Tokushima less so IMO. I don't know Matsuyama yet. All over the island, there are some lovely trails in the mountains - many are well marked because they form part of the 88 temple pilgrimage routes. The Iya valley is supposed to be especially beautiful. Needless to say, it's one of the harder places to access.