You can participate in countdown events. There are multiple countdown events held in Tokyo, too.
Or, you can visit temples to ring "Joya No Kane". It's a custom to struck huge bell in temples 108 times in the new years eve.
some more things to do are listed here:
Visit shrines on new years day. Shrines are extremely crowded but we have a tradition to visit shrines to wish for luck in the new year. It's called "Hatsumode".
Destinations best for Hastumode:
Some other things to do: