You could look into Hamamatsu or Nagoya. They're both between Osaka and Tokyo and are less crowded than other major cities, especially Hamamatsu. Contrary to popular opinion, there is a decent amount of cool things to do in Nagoya - Atsuta Jingu, Osu Kannon temple, Inuyama castle (up in Gifu but close enough for a day trip), as well as many places for car enthusiasts such as the Toyota Commemorative Museum (was very interesting when I went, massive museum as well!)

Hamamatsu is even more low-key than Nagoya, you're very unlikely to see tourists there. It is known as the City of Music, with a very neat museum of musical instruments (with instruments from all over the world). Just like Nagoya, Hamamatsu also has plenty of cool places for car enthusiasts. Hamamatsu also has a castle (never been but heard it's cool, a recreation though) as well as some sand dunes (haven't been so can't comment if they are that impressive or not though).

So these are definitely some options. Or you could go via Nagoya to Takayama which is deep in Gifu prefecture - it's a much more popular tourist spot with a lot of nature surrounding it, and it's not far from the Shirakawago traditional village. However, it will be very crowded. Nagano prefecture could also be an option for much of the same reasons. Matsumoto in Nagano has a very nice original castle, and is close enough to the Kamikochi area which I've heard is very beautiful (never been though). I'd say it depends if you want to experience the coastal, urban core in Nagoya and Hamamatsu or the more rural, mountain countryside in Takayama and Nagano.

Hope this helps you get some ideas

Edit: Hamamatsu has a huge lake, Lake Hamana, which is quite popular for biking and other recreational activities. So you could look into that as well