10 dramas that have a quiet feel to them. It doesn't have to be the whole thing, all the time, but good chunks need to give you a sense of quiet, almost melancholy. Avoid boring or dull. A highly subjective topic, based on how you felt at the time of watching so if the drama you have in mind gave you something like described, then great, I look forward to reading it.
1. Something in the Rain - lots of the drama (when FL's mother or ex isn't being nasty or...) there are simple scenes: eating in a restaurant with soft music, walking in the rain, sitting in the car or at home hanging out; all accompanied with quiet music.