Mostly watch Korean dramas than Japanese. Heres a list of some of my personal favorites:
A Bird That Doesn't Cry
Bread, Love and Dreams
Woman of the Sun
First Love Again
Boys Over Flowers
Secret of my Love
Love, My Love
The Moon Embracing The Sun
Queen for Seven Days
The Fugitive of Joseon
Witch at Court
I watch a lot of my K-dramas on a channel called KBS World. X3
My girlfriend is a gumiho (9 tailed fox). Has amazing music and it's hella cute fam
I've found Hero Yoshihiko to be extremely good, however in the third season some episodes the subtitles were badly timed and I couldn't find other versions of it...
I watched Final Fantasy Dad of Light too, it's a touching story about how a guy tries to reconnect with his dad through FFXIV but in general it likes to deal with common social interaction issues and how to solve them (and it's on netflix)
for japanese dramas, i’ve only watched two which are sukina hito ga iru koto and hana yori dango. for korean dramas, i recommend love in the moonlight, w, and strong woman do bong-soon.
I'm more interested in dramas with good OST, ballads mostly.