What's particular in January around Tokyo might be below:
- ice skating
Some shopping malls build ice skate links during winter. Such as Tokyo Sky Tree and Akasaka Sacas.
- winter illumination
In other words, Christmas Lights. Some places put up Christmas Lights until January. Those lights are beautiful especially Marunouchi area, near Tokyo Station.
- Enjoy winter delicacies
Such as Oden, hot sake, Nikuman (pork bun), hot pot dishes, etc.
Ramen feels more delicious in winter because outside is very cold.
You can find some more information from below:
10 Best Things to Do Limited in Winter in Tokyo https://hubjapan.io/articles/how-to-enjoy-your-winter-in-tokyo
14 Best Winter Japanese Food You Should Taste https://hubjapan.io/articles/the-best-japanese-food-you-should-taste-in-winter