On my way to Kyushu, I took the train to Nagoya for an afternoon flight to Kagoshima. I had time to visit Nagoya Castle before going to the airport. The Castle is just a short subway ride from the JR station and the entrance fee is 500 yen. I highly recommend visiting!
The Nagoya Castle Hommaru Palace restoration is fabulous. The palace was originally built in 1615 and was used as a residence and government office of the Lord of the Owari Province. You have to remove your shoes and flash photos aren't permitted.
The original castle was built on the orders of Ieyasu Tokugawa to secure a position on the Tokaido road and to ward off attacks coming from the direction of Osaka. It was completed in 1612. Most of it was destroyed in WWII. Three corner towers, three gates and most of the paintings on the sliding doors and walls in the Hommaru Palace survived and the rest was reconstructed. The inside of the castle (7 floors) is a big museum, with many exhibits and an observation area at the top.
You can find the English brochure about the castle here.