Planning the First Japan Holidays

What is the best way to travel :

1. Hakone to Takayama

2. Takayama to Kyoto

3. Hiroshima to Osaka

4. Osaka to Narita Airport

I will be purchasing a 14 day JAL Pass. Can i use the pass for theabove?
Thank you

This type of information is all available on this website!

Hakone to Takayama

Take the shinkansen from Odawara or Mishima (near Hakone) to Nagoya and then the limited express train to Takayama:
http://www.hyperdia.com/

Takayama to Kyoto

http://www.japan-guide.com/e/e5908.html?aFROM=2158_5900

Hiroshima to Osaka

http://www.japan-guide.com/e/e3404.html?aFROM=2157_2160

Osaka to Narita Airport

There are direct flights from both Osaka's Itami Airport and Kansai Airport to Narita Airport.

How to get to Itami Airport:
http://www.japan-guide.com/e/e2433.html

Kansai Airport:
http://www.japan-guide.com/e/e2033.html

Alternatively, take the shinkansen and Narita Express via Shinagawa Station:
http://www.hyperdia.com/

I will be purchasing a 14 day JAL Pass. Can i use the pass for theabove?

Assuming you mean the Japan Rail Pass, yes, the pass can be used for all the above sections (except for the short section from from Hakone to Odawara or Mishima) if you use JR trains (except nozomi).