Dramas that I'd recommend without hesitation:
Virgin Road (romcom, family drama)
News no Onna (workplace and family drama, I guess?)
Hakusen Nagashi (school)
Ice World (romance, crime thriller)
Dramas that I liked personally but not as good as the rest:
Cheap Love (romance)
With Love (romance, of sorts?)
Hitorigurashi (romance)
Tabloid (crime thriller)
Dramas that were objectively good--the iconic Jdramas of the 90s, I guess--but I'm petty and I don't like their ending:
Tokyo Love Story (romance)
Over Time (friendship, romance)