Shedule approval, 9 day travel

Thank You for your time. I dont have much money but Im saving to Japan, Ive read all I can on this excellent site and I came up with this schedule. So please tell me is this the best and cheap way to travel. Im planning to buy Japan Rail pass, but since I have 7 days and my trip is for 9 I thought using it the first 7 and pay for the last two steps, is there a better way? please advice. Another thing, I was planning my for January 5th is this a cheap season or should I travel some other time?

1 Narita Tokyo
2 Tokyo
3 Tokyo Nikko Tokyo
4 Tokyo Kamakura Tokyo
5 Tokyo Mt. Fuji, Hakone Kyoto
6 Kyoto
7 Kyoto Himeji Kyoto
8 Kyoto Nara Kyoto
9 Kyoto Osaka Airport

Thank you so much, I will appreciate any comment.

Regular tickets will come cheaper than a rail pass!

On day 5, there is enough time to visit the Fuji Five Lake region or Hakone, but not both.