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If there's one event you must see in Nanao, it's this one! Taking place during Golden Week on May 3, 4, and 5th, this festival is designated as Japan's Important Intangible Cultural Property and consists of pulling massive structures called Dekayama ("Huge Mountain") through the streets of Nanao. These Dekayama are as high as 12 meters and weigh almost 20 tons, and the diameter of their wheels is 2 meters. Apart from the size of Dekayama, changing the direction of huge creaking wheels with the help of ropes and a central fifth wheel located underneath the float is an event unto itself. Anyone is welcome to have a hand at pulling one of the three floats through the narrow city streets during the 3-day event, so have a try at it!
石川県能登島ガラス美術館
This museum is the only public specialized glass art museum in Japan. It displays some unique glass sculptures based on original ideas from artists such as Picasso and Chagall. It also has some interesting sculptures and a section devoted to old liquor bottles once used in Japan. If that wasn't quirky enough, the building looks like a ship straight out of Star Wars.
石川県七尾美術館
Nanao was the birthplace of Tohaku Hasegawa (長谷川等伯), who was a well known Japanese master painter. They have annual exhibitions related to his works. You can also see many local artists' works there. Worth checking out if you have some free time.
七尾城山
Contrary to the name, this area contains very little in the way of castle ruins, offering just a small section of stone wall that was once used to fortify the small castle. The reason to go is not for the (non-existent) castle, but for the best view of Nanao and its bay. The small park at the top is peaceful, and the view is gorgeous. The best time to go is in spring on a clear day.