Travel advice needed between Nagoya and Tokyo

Dear all,

This summer (mid July - beginning August) my boyfriend and I are travelling around Japan. We are starting of in the Osaka / Kyoto region. Then we are off to Nagoya (I am presenting in a conference there) and we're finishing in Tokyo.

We have about 2 days to spare, somewhere between Nagoya and Tokyo. Any advice on where to go?

We were considering the Shikuoka region, Hakone, Fuji five lakes, Izu Peninsula, Atomi or climbing Mt. Fuji. Do any of these particularly stand out or do you have any other advice?

We are travelling by local train and we're specifically interested in culture, history, food or hiking. Not so much interested in modern areas/shopping malls/etc.

Thank you for your help!

Kind regards,
Marike

Here's a website about tours around Nagoya for your reference:

http://tourguides.nagoya/en/index.html