which pass should i purchase

Tokyo - Takayama
takayama - kyoto
kyoto - tokyo

thank you so much ! :)

If you do the long-distance trips (Tokyo-Takayama, Takayama-Kyoto, Kyoto-Tokyo) within 7 days, a 7-day Japan Rail Pass will be considerable cheaper than regular train tickets. A 14-day pass does not pay off.

Thank you, Uji ! :)

Have a nice day !

There is another option, if you are willing to take a bus. You could get a three day Japan bus pass, and buy round tickets from Nagoya to Takayama on the Nohi bus line. The Japan 3 day bus pass is 10,000 yen, and the round trip to Nagoya is about 3000 yen. This is about half the price of a 7 day JR pass. The three day pass can be for non-consecutive days, and if your travel is over 7 days, this is a very good option.

You would be going:
Tokyo to Nagoya, Nagoya to Takayama.
Takayama to Nagoya, Nagoya to Kyoto.
Kyoto to Tokyo.

By the way, this is also the trip plan if you use the JR Pass. On both methods of transportation, you stop at Nagoya to switch busses or trains. Here are the links for the busses.

http://www.japan-guide.com/e/e2369.html
http://www.nouhibus.co.jp/english/

The intangible that is not covered is that the JR pass is active for seven days, and you can use it for side trips, such as Kyoto to Nara and back. The bus method just coveres the three days that you travel.

Thank you so much ! ebaychucky311 :)