What to do in Chubu?

I'm going to Japan in December. Since it's winter and the Alpine Route is closed, what else can I do? I'm spending a night at Mt Fuji.

Here are some ideas:
http://www.japan-guide.com/list/e1104.html

Thanks Uji. Perhaps, let me share more on my plans when I'm in Japan. I'll be in Japan for 15 days. Arriving in Narita and departing from Osaka in early December. My plan is to spend 2 nights in Tokyo, 1 night in Mt Fuji/Fuji Five Lakes, 2 nights in Chubu, 3 nights in Kyoto, 1 night in Mt Koya, 1 night in Wakayama, 2 nights in Hiroshima and finally 2 nights in Osaka.

I'm keen to spend time with locals and see how they live. I love history and museums, and nature. Where possible, i prefer to avoid shopping centres.

My plan was to check out the Alpine route. To me, it's nature at work and I'm quite fascinated. However, since the route will be closed during winter, i'm lost for places to go.

Do you have any recommendation for me? Thanks.

This is a nice way to meet some locals:
http://www.nagomivisit.com/

I recommend a visit to the snow monkeys instead of the Alpine Route:
http://www.japan-guide.com/e/e6028.html

Nagoya is always nice, but Toyohashi nearby is a smaller city you might check out for some museums and onsen. Gifu also has a more laid-back mountain lifestyle, but each time I went I was staying with locals instead of sightseeing, so I don't have many tips there!
If you like samurai, Hikone and Sekigahara could be done in the same day.

Thanks Uji and Buri0110 for the recommendations. I'm quite excited about interacting with the locals over a simple meal. Will check it out certainly.

On a side note, I'll be on the move. For the footwear, will a normal pair of sports shoes be sufficient or is it recommended that I wear boots instead?

Thank you!