If you're around Tokyo during the New Year, be sure check out the Emperor's New Year Greeting. This is a yearly event where the Imperial Family makes several appearances throughout the day (see below for times).
Be sure to get there a little before the scheduled appearance, as you'll have to go through security checks and lines can be long.
Make sure to take tons of photos of the Palace up close, as this is 1 of only 2 occasions where the inner grounds of Tokyo's Imperial Palace is open to the public. The other being on December 23rd for the Emperor's birthday.