Here's what some Wikipedia searches led me to:

The Daiō Wasabi Farm (大王わさび農場, Daiō Wasabi Nōjō?) is a wasabi farm established in 1915[1] and located in Azumino, Nagano Prefecture near the center of Honshū, the main island of Japan.[2] It is a popular tourist spot due to its beautiful watermills and for the river that runs through it.[2] A restaurant offers wasabi-flavoured ice cream and other wasabi-themed products.[1] Outside of Japan, the site is best known for its appearance in the 1990 film Dreams by world famous director Akira Kurosawa in the segment called "Village of the Watermills".[2] Daiō is one of Japan's largest farms—and its largest wasabi farm—covering 15 hectares.[2][3]

I did some more searching and discovered that Azumino is a city formed by the merger of several villages just north of Matsumoto. I know that there are frequent trains from Tokyo's Shinjuku Station to Matsumoto (Chuo Line), but it looks as if you have to switch to local trains or buses from there. It would about 2.5 hours from Shinjuku to Matsumoto.

This route is in fact an option for traveling between Tokyo and Kyoto. From Matsumoto, you continue to Nagoya and pick up the Shinkansen for Kyoto there.