Nagoya is one of the best bases for day trips in central Japan. Inuyama is the easiest — 30 minutes by Meitetsu train — and combines an original Edo-period castle, the open-air Meiji-Mura museum, and summer cormorant fishing on the Kiso River.
Beyond Inuyama, the preserved Edo-era post town of Magome in the Kiso valley is reachable in under two hours by shinkansen and bus, and pairs well with a walk along the old Nakasendo road to Tsumago. The Grand Shrine of Ise — one of Shinto's most important sites — is 90 minutes south by Kintetsu limited express. The Toyota factory tour at Toyota City (book ahead) is half an hour by JR.