Hi there,
All of the routes you plan to travel are straightforward and easy, still there are a couple of points that are good to know.
Starting with travel from Tokyo - Hakone, the Shinkansen station for Hakone is called Odawara. From there local transport runs throughout the area. It's mostly important to know the name of this station.
From Hakone - Kyoto, return to Odawara from where you can use the Shinkansen directly to Kyoto station.
Kyoto - Takayama, this is a pleasant trip to make. Use the Shinkansen from Kyoto to Nagoya and transfer there to the Hida Wide View express bound for Takayama. The route between Nagoya and Takayama is travelled through a mountain pass and very scenic. There are also a very limited amount of Hide Wide view trains that start in Kyoto and go all the way to Takayama.
Takayama to Tokyo. There are two options here, one is to return to Nagoya with the Hida Wide view express and from Nagoya use the Shinkansen back to Tokyo.
The 2nd option is to use the Hida Wide view express up towards Toyama and from there use the new Hokuriku Shinkansen to Tokyo.
Both routes are about the same in travel time, it depends a little on what time of day you travel. My recommendation would be to take the 2nd, as it would give you a different view instead of travelling the same route back to Tokyo. Here are some examples for Takayama - Toyama - Tokyo.
Hope this helps,
Daniel