As I recall, the subway signs in Nagoya are bilingual. In fact, that's true of every urban subway and commuter train system that I have encountered.

Japanese buses often are labeled in Japanese only, and the occasional country train station will have nothing but its name in Roman letters, but if you stick to the major cities, you won't have much trouble.

If you're going to spend a fair amount of time in Nagoya, Kodansha International's "Kyoto-Osaka: A Bilingual Atlas" has a section with pretty good maps of central Nagoya and public transit for the metropolitan area. In addition, most largish Japanese cities have tourist information centers (kankou annaijo) with English-language maps of how to get to the sights. If the counter attendant doesn't understand "English map" spoken slowly and clearly, ask for "eigo no chizu" (ay-go no chee-zoo).

If the counter attendant crosses his/her arms in an X-shape or waves a hand back and forth in front of his/her face, that means "no."