If you’re interested in older J-dramas Rare Doramas https://raredoramas.info is an excellent site. Recent changes at subtitle sites might make it a little harder to match the shows, although many of the 70s and 80s shows are hard subbed. As with most shows from that time, film quality tends to be poor.
I’ve watched very few shows from before 2000. But
Glass Mask 1997 (11) J - about an up and coming actress and her relationship with her mentor. Has a sequel .
GTO 1999 (12) J - is a highly rated school drama that has been in my plan to watch list for a while.
Sukeban Deka 1985 (24) J - very episodic show about yo-yo wielding high schooler who works with the police to fight gangs and corruption in the schools. Unfortunately only Season 1 is fully subbed.
Dai Chusingura 1971 (52) J - story of the 47 Ronin starring Toshiro Mifune
Zatoichi The Blind Swordsman 1974 (26) J - about a blind masseuse, gambler, and swordsman. 26 movies and 100 TV episodes. Now that I’ve watched all the original movies I’m ready for Season 2.
As for Korean, I’ve watched nothing before 2005.
My Love Sam Soon 2005 (16) k is one of the highest rated k-dramas ever.