Subete ga F ni Naru 
Itazura na Kiss - Love in Tokyo.  I thoroughly enjoyed "Playful Kiss" korean version, then found the taiwanese one "it started with a kiss" so went searching to see if there was a Japanese version & found it.& that started me on Japanese dramas - yeh!
Bloody Monday! And i loved it! I actually found it by Accident, I googled the name of the manga (bc my library didn't have all of the tomes) I should watch it again, but dunno if I would get the same feels after having watched dozens and dozens of others Jdrama ^-^ 
I'm a bit disappointing in myself for not really remembering what my first Japanese drama was.. I just kinda gradually moved from anime to live action dramas so I guess it very possibly could be Hana Yori Dango?
hanazakari no kimitachi e ^^ 
mine was Nigeru wa Haji da ga Yaku ni Tatsu!
My first Japanese drama was Mischievous Kiss: Love in Tokyo. It's pretty good. I enjoyed it a lot!
Subete ga F ni Naru