The city of Hida Furukawa is one of the most relaxing places I've ever been in Japan. You can reach Furukawa by car, bus or JR. The train in my opinion is the best way to reach the city from Takayama within 15 minutes, free if you have the JR pass.
Furukawa is a small tranquil city but if you are curious there is a lot to see and discover. From the mighty craftsman "Hida no Takumi"museum and their works all around, the eccentric night festival of Hida Furukawa (only in April), it's beautiful floats (Yatai), the local food like the Hida ramen, two great sake breweries Kaba and Watanabe, the so bright Shirakabe Dozogai with it's white walls and carps floating in the torrent, on the side of the road (carps only and spring - first period of autumn),  an ancient and interesting tradition of candle making and much more...Furthermore since 2016 Hida Furukawa got even more popular thanks to the animation movie called "Kimi no na wa." (君の名は), letterally "Your name."  written and directed by Makoto Shinkai, where the city glimpse inspired the scene of this movie. So come with me and let's discover Hida Furukawa together!