As you may know, Nagoya is the capital city of Aichi prefecture.
Nagoya is the 3rd (some may say the 4th) largest city in Japan, and you can enjoy shopping, visiting cultural museum, trying many delisious dishes! You can probabry find a lot of information about the city center from the websites or lonley planet. I would like to focus on the city later as well.
Nagoya Info:
http://www.nagoya-info.jp/en/ (Japanese, English, Korean, Chinese, Thai are available)
However, I would like to introduce you to the places where you can take a short trip from Nagoya for a while.
Inuyama-city (犬山市）
http://ml.inuyama.gr.jp/en/
Inuyama, the city where you can experience traditional Japanese life.
You can get there by Meitetsu train from Nagoya station by 30 min! What a good access!!
If you come to Japan, you want to see one of old castls, right? Yes, there is one in Inuyama, Inuyama castle. (pictures are coming) It's about 10 minutes walk from Inuyama-Yuen station. From the station to the castle, there are old shopping areas called "Sho-ten-gai". There are not much to buy for tourist, but fun to see and walk through. You can probably see Japanese people shopping for there lunch or something.
Also, there are some modern Japanese style cafe to sit and rest if you get tired.
http://ml.inuyama.gr.jp/en/tourist-facilities/cafes-and-restaurants-en
It usually costs less than 1,000 yen per person for a drink. (100 yen ≒ 1 doller)
Around the Inuyama castle, there are a place you can experience Maccha tea; Japanese traditional green tea with a ceremony. We don't sweaten green tea, so you may feel a bit bitter, but I hope you can try the real taste of the tea. But don't worry! It always comes with a sweet Japanese cake. This is non meat or alcohol, so I believe all people with any religions can enjoy!
