One of my favorite day trips from Nagoya is to Magome and Tsumago in Nagano Prefecture. They are two restored and preserved Edo-period way stations on the Nakasendo in Nagano Prefecture. Nakasando is similar to the more famous Tokaido, both very old roads that connected Kyoto with what is now Tokyo. The two and half hours it takes to walk between the two stations is filled with very historic buildings and scenery reminiscent of the Edo period, except for the slightly more touristy feel of Magome, which boasts a plethora of good places to eat and buy knick knacks.
See a longer article about this destination on the Japan Visitor Blog
Here is a video that will give you some idea about what you can see on a trip to Magome and Tsumago.