5 places in 6 days... it's reaaaaaaly rush, please note it first.
Well, I'll start in the case you start from Narita or Haneda.
I suggest this itinerary as following;
4.Osaka & Kyoto
This is just a plan of the order to save your time as much as possible, but it might be changed depend on
1) Where you spend on the new year's eve and the new year's day
2) Where you fly back from
Following is just the information for you of the transportation and the timetables, reservation forms.
1. Shinjuku to Kawaguchiko (NOTE: the timetable for Dec is not available yet. Check out in Oct.)
> approx 2 hours
2.Kawaguchiko to Shirakawago
First you have to get to Takayama then take another bus to Shirakawago.
> approx 6 hours total
3.Takayama to Osaka & Kyoto
>approx 4 hours
Kyoto comes first so you can get off and take hotel in Kyoto to explore around including Osaka.
Between Osaka and Kyoto takes only 30 mins by local train.
If you fly back from Tokyo, the you can take Shinkansen from Osaka, or airplane from Itami or Kansai international airport, both in Osaka.
But I recommed Shinkansen since the airport is a bit far from the heart of Osaka area, you have to change trains several times with your luggage.
Hope this can be your help and always welcome for further questions!