[Sangetsu]

Book your hotels now, if you haven't already. You can stay as far away as Osaka if you have to, Kyoto is not far by train. More than likely you'll see foreigners at the train station or other places. Don't feel shy about talking to them, many of them enjoy the opportunity to speak to other foreigners in their own language. Hotels in Tokyo will be easier to find during the holiday as many people will leave the city and return to their home towns.

Kyoto would be the best place to spend New Year's eve and day. Where I live, there is a tall hill which has a wonderful view to the east. Many people climb the hill to view the first sunrise of the year, and a local restaurant serves free osechi to anyone who wants some.

Tokyo doesn't slow down much for the holidays, you'll find plenty of places open for business.

You'll have no problem traveling alone, it's perfectly safe here. Wear very comfortable shoes, a backpack, and a camera, and enjoy your stay. If you are interested in seeing places in the Tokyo area, feel free to PM me, I can tell you where to go and how to get there.