Try the following tour, recommended by residents or metro enthusiasts:
Make sure to include Linimo in your tour. It's one of very few Maglev metro lines in the world. To reach Linimo, take Higashiyama Line to Fujigaoka terminus. Nagoya's Metro Museum is at Akaike terminus of Tsurumai Line.
Nagoya City Tram & Subway Museum. This museum is filled with vintage trains and trams, photographic history, hands-on simulators, and even giant tunneling equipment. Address: Located on route 153, a 7-minute walk from exit 2 of Akaike Station. At Akaike metro station. Hours (check before visiting): 10:00 to 16:00, closed Wednesdays and from 12/29 to 1/3. Admission: free. Reference: nic-nagoya.or.jp.