Nagoya's subway is small (six lines) but covers the centre well. The Higashiyama (yellow) line runs east-west, linking Nagoya Station, Fushimi, Sakae and Higashiyama Park. The Meijo (purple) line is a circle that takes in the castle, Sakae and the port. A one-day Donichi Eco Kippu costs around 600 yen and is valid on the metro and city buses on weekends and public holidays — the cheapest way to cover the sights.
For longer trips out (to Inuyama, Toyota, the airport) you'll use Meitetsu or JR private rail lines. Manaca and Suica IC cards work on all of them. Taxis are plentiful but expensive; bicycles work well on the flat city grid, and the city has several bike-share docks.