I didnt watch a lot of Japanese dramas. Those are among my favourite dramas of all time, some are very old though:
https://mydramalist.com/2-1-litre-no-namida -very sad
https://mydramalist.com/1344-asuko-march -quite interesting plot about a girl who goes in the technical high school with mostly "bad boys" and bad reputation
https://mydramalist.com/11189-dear-sister -sisterhood/family drama
https://mydramalist.com/25-gokusen -quite interesting imo, about new teacher who becomes homeroom teacher of the worst class. And she is a heir of the yakuza clan too. There is a lot dramas with similar plot, if you like those types, I can recommend you more.
https://mydramalist.com/51965-koi-wa-tsuzuku-yo-doko-made-mo -GREAT drama and newer than any in this list. You should definitely watch it.
https://mydramalist.com/56-tatta-hitotsu-no-koi - I LOVE this drama. I find it very romantic and simple, but amazing in it's simplicity. It is very old though... Rich FL/poor ML
Those are my favourites. You have also dramas which almost everyone watched first like Hana Yori Dango, Hana Kimi, Itazura na kiss and such... But I, personally, dont find Japanese versions of it the best. Maybe only this 1 https://mydramalist.com/2985-hanazakari-no-kimitachi-e