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As a Philippines citizen, you will need a visa to visit Japan (this is true whether or not you are a US resident). You can find all the visa information you'll need from the Japanese Consulate in Los Angeles, particularly the page on short-term visas.
For tourism/sightseeing visas, there's a list of required documents for a visa. Complete all that, and take it to the consulate for a visa.
If you do obtain US citizenship in the future, you'll be able to visit Japan for up to 90 days for tourism or business visa-free.