Eyes Of Dawn (1991) is a classic and my favorite followed by Star In My Heart of the very few from the 90's I watched. I also really enjoyed family dramas A Love Without Fear (1992) and Scent Of Love (1994) and the college theme Kwangki (1999).
I honesty don't if they can't been found just to watch anymore, I downloaded a few of these titles from DVD/HQ versions with eng subs many years ago and the websites no longer exits or links worked. I've watched a few SBS ones from the 90's/early 2000's on their VOD website for free . KBS has been uploading some 80's and early 90's ones on you tube on the last few months on their classic channel but everything in both websites is in Korean only no eng subs, I haven't seen any of these yet but many seem to be long dramas.
I love Japanese and Thai dramas from the 90's more but some Korean have been interesting to watch, specially with the older actors in their younger days.
