My wife and I have the following itinerary in mind:
Day 1: Tokyo (arrival) - transfer to Hiroshima
Day 2: Hiroshima
Day 3: Hiroshima - Osaka
Day 4: Osaka
Day 5: Osaka - Kyoto
Day 6: Kyoto
Day 7: Kyoto - (daytrip Nara)
Day 8: Kyoto - (daytrip Okayama)
Day 9: Kyoto
Day 10: Kyoto - Takayama
Day 11: Takayma - Tokyo
Day 12: Tokyo- (daytrip Disney World)
Day 13: Tokyo- (daytrip Disney Sea)
Day 14: Tokyo - (day trip Hakone)
Day 15: Osaka - (day trip Nikko)
Day 16: Tokyo -
Day 17: Tokyo -
Day 18: Tokyo
Day 19: Tokyo
Day 20: Tokyo
We are planning to buy a 14 day JR pass, would this pass cover all the different routes mentioned? Is it worth buying the 14 day pass or the 21 ?
Is it feasible to travel from Kyoto to Takayama in one day?
Are we spending enough time at each of the different destinations, or are there any changes to the itinerary you would recommended?
The most economical and best use of travel for you would be a 14 day Rail Pass, used from days 1-14, and going to Nikko during one of the last days (12, 13 or 14). The Pass would not cover getting all the way to Hakone, so use a Hakone Free Pass for that instead. For the rest of your time in Tokyo, look into a 3 day subway pass and if you depart from Narita, then there is a cheap 1000 yen bus.
Choosing Okayama is an interesting one - few go to see its sights, including its castle, but also one of Japan's Top 3 Gardens, Korakuen, plus the beautiful Handayama Garden. Going over to see Konpirasan in Kotohira, Kagawa is another choice for a magnificent and ancient mountain trek for the view and shrine.