Hi,
70% of Japan is made of forests, narrow valleys and paddies. You will find anywhere nice hiking trails and small villages. I am more familiar with the Tokyo area, but I am sure you will find similar places around Nagoya (to know more about hiking in Japan, you may refer to this story (
Hikes outside Tokyo)
From Nagoya, you are also not very far from Shizuoka-ken. Izu peninsula has a great shoreline. The oigawa valley, and its old steam train, is also very interesting.
I hope this helps