travelling Honshu 21 days

Hi Qing,

That looks like one amazing trip! I've to say that at the same time it may be hard to find the best route or pass because of the amount of places involved. As general advice, I would try to plan expansive rail travel not too far apart, this way you can make the most of a JR Pass and maximize your savings, some of the more pricey travel parts include a visit from Osaka to Hiroshima (¥ 21,040), side trip to Takayama (¥11,680) and a visit to Nikko (¥10,860).

A 7 day JR Pass would for sure come in handy for the period from the 27th of Dec - 2nd of Jan. This because you could cover the following routes:

Osaka - Hiroshima ¥ 21,040 (return)
Hiroshima - Miyajima ¥ 1,140(return)
Osaka - Kyoto ¥ 540
Kyoto - Nara ¥ 1,380 (return)
Kyoto - Kanazawa ¥ 6,710

For a total of ¥ 30,810 the 7 day JR Pass is (¥28,300).
and a possible side trip to Takayama adding an additional ¥11,680 in savings.

From Kanazawa you can take the train to Hakuba 212 Minutes / ¥ 5,550 (including 2 transfers). Than from Hakuba you can take a bus to Nagano and from Nagano the bus to Nozawa, this takes about 2H, you can also take the train but this takes about 5 hours and involves multiple transfers but is covered by the JR Pass. From Nozawa it is easy to take a bus back to Nagano and from there take the Shinkansen to Tokyo.
An other option would be to go for a 14 day JR Pass, you could use it from the 27th until the 9th and cover most of your train travel with it, I think that you would most likely be savings a nice amount of money but it really comes down to the actual amount of travel that you will make.

Going back to your first question and arrival at Kansai Airport, the best way to get from here to Namba is to take the Nankai Ltd. express which travels there directly and takes 37 Minutes / ¥ 1,390. You can buy a ticket for this directly at Kansai Airport.

Once you are in Osaka you can certainly consider a visit to Kobe but there will be more than enough to see in Osaka as well. I would recommend making a list of what you wish to see most and decide on that.

Staying at Kyoto around new year? This is a good question and hard to answer, I would probably stay in Kyoto myself for two reasons, one is that travelings around new year can be really busy because many Japanese travel around to country to visit family. The 2nd is that Kyoto is perhaps the place the experience the way how New Years day is celebrated in Japan. It is common for Japanese to visit local temples and preform different rituals (such as ringing the temple bell) and festivities related to the new year (such as Otoshi dama). As a foreigner this can be very interesting to observe and you can easily join in, in addition you may find that some Japanese may react a little surprised when a foreigner participates in Japanese customs but it's always a great experience.
Than again if you do have a JR Pass it may be better to travel around to make the most of your pass.

It's a lot so I hope I covered all of your question,
Daniel