Japan is on which side of USA (eastern or western)?

Both. Cardinal directions are a two-dimensional idea, so in three dimensions (especially when referencing spherical items), they can run into each other.

Conventionally, the "north" and "south" of the earth are well-established as they represent the earth's poles. However, there is less of a distinction for east and west. Even with north and south you still run into the problem that the earth is round.

https://en.wikipedia.org/wiki/Cardinal_direction#Usefulness_of_cardinal_points

Traditionally, Japan is considered to be east of the U.S. even though it's closer to our West Coast than our East Coast. For centuries, it was considered to be in the farthest reaches of the "Orient." That term is no longer in good taste, but we do still say it's located in "East Asia."

I think most people would say Japan lies east of the U.S.
https://en.wikipedia.org/wiki/Orient#History_of_the_term

6730 miles from Tokyo to New York City. https://www.timeanddate.com/worldclock/distanceresult.html?p1=2416&p2=248

5151 miles from Tokyo to San Francisco. https://www.timeanddate.com/worldclock/distanceresult.html?p1=224&p2=248

Tokyo is much closer to Honolulu and Anchorage than to SF.