As Richard points out, Takayama and Matsumoto are much more accessible from Nagoya or even Osaka than from Tokyo.
If the OP plans goes to Matsumoto at all and is starting his trip from Tokyo, then Matsumoto is readily accessable from Tokyo via Shinjuku Station. However, considering time constraints I'm not sure if the OP should visit Matsumoto but spend more time visiting Takayama. Which in that case I would go to via Nagoya Station from Tokyo.