I can't really answer you question sorry, but fore some reason I remembered the drama Soulmate (2008 i think), and it has a really nice soundtrack that maybe you'll like to check out. I don't know, I get this intuition feeling lol. I don't really know your taste in dramas, but that was a really nice different style drama too !!!!!
I don't specifically have any recommendations but want to share a link to a good source on Korean indie music:
Just typing indie into the Seoulbeats wesbite search bar yields tons of results like interviews with K-Indie artists, a section highlighting these artists and their discography called KPOP Indie Gem, and etc: http://seoulbeats.com/?s=indie&x=0&y=0
@nikonim No problem! Also, I really enjoy the indie electro-house trio Mad Soul Child .... Jinsil, the vocalist, has an amazing voice! They've done a lot of collabs with k-rappers and OSTs for movies/dramas.
You have the band Annyeongbada (I personally like them a lot), Outsider with the song Bye U, 2000 Won with Goodbam and another song is called
Beautiful ft. Ailee. I also recommend you to look at the youtubers Simon and Martina, when you go to their playlist and scroll down a little you will have playlists with korean indie songs.
NELL of course. I also love Yukari/aseul, Neon Bunny, Heo, Goldmund, Jang Kiha(!)... The Koxx good rock band, and of course Thorn Apple, and lovely Fromm they are awesome! I gotta check my pendrive, i have so many indie bands there...
Also if you want to try some experimental music (mix of traditional Korean music and electro-rock in this case) Jambinai will grab your attention. https://www.youtube.com/watch?v=aik3JRXud6Q
Some of my personal favourites have already been mentioned here - The Black Skirts, Hyukoh, Nell, Standing Egg. But here are some more that you might want to give a listen to- 10cm, Urban Zakapa, Clazziquai Project.