Having just spent some time in Takayama over the weekend - I can tell you that it's a nice little town, but it's way off the beaten track:

Journey from Tokyo to Takayama = at least 4hrs 49mins
(Minimum 5hrs 10 mins if you're using a JR pass)

Journey from Takayama to Kyoto = at least 3hrs 41mins
(Minimum 3hrs 50 mins if you're using a JR pass)

That is a lot of travel in order to spend one day in Takayama. The train journey from Nagoya to Takayama is quite pretty... but it might not be the best investment of time.

Don't get me wrong - I think Takayama is a nice town. I'd say it's good for a full day of sightseeing (but not more). It gets plenty of Japanese tourists and it deserves more foreign visitors. I would really love to spend some time touring Takayama, Shirakawa-go, some hot springs around Oku Hida or Gero, then Kanazawa, and the Noto peninsular.... but a day trip just doesn't cut it for me.

If this is your first visit to Japan, then my guess is that you'd get a better "return" on your time if you were to skip Takayama and make a day trip from Tokyo to Kamakura or Nikko instead.

If you took Takayama out of your plan, what would you miss?
- You would not get a chance to see the Takayama "old town" - a series of low, wooden shop fronts along two or three streets in the style that would have been common in the 19th century.
- You would miss the morning markets, which are nice markets. (assuming that you arrive early enough to see them)
- You would miss the impressive Takayama Jinya, which was the outpost of the Tokugawa administration during the Tokugawa bakufu.
- You would miss some temples.
- You would miss a nice park with preserved old buildings.
- You would miss a nice train journey.

It's not insignificant - I know - but even so, I think the old shop fronts exist in parts of Kyoto, the markets (and that kind of atmosphere) can be found in Kyoto and Tokyo, the temples are less impressive than what you can see in Kamakura, Nikko, Kyoto and Nara....well you get my drift.