Most countries, including the Japan and the US, recognize a patent in another country for filing purposes. Which is to say, if you need to sue someone in Japan, yes you need a patent in Japan. However, you bring your US patent to the Japan Patent Office and they consider that as your file date and so you can sue for infringements that happen before your patent in Japan was issued.

If this is actually useful for you, of course, you need a patent lawyer in the specific country you're talking about, which is not cheap, and that's why the other posters said millions of dollars. Patents are not worth it for most people because you still have to pay lawyers to get anything out of them. You also pay for your time in court, acting as witness and testifying and watching court proceedings instead of doing your own business.

Fair point