I really like indie films and things that are kind of unconventional, artsy, and dreamy.
  • Example of movies: I'm a Cyborg, But Thats Ok, Air Doll, Norwegian Wood
  • Example of dramas: I thought Heart To Heart and It's Okay, Thats Love both had a nice indie vibe to them
I primarily watch kdramas, but I'll pretty much watch anything.

Thank you!
hmm...not sure about dreamy feel, but some of korean indie films are:

3-Iron
Bleak Night
Spring, Summer, Fall, Winter... and Spring
Peppermint Candy
Woman is the Future of Man
The Journals of Musan
Light shines only there
Parade
A drift in Tokyo
Backwater
Oishii Man
The kirishima thing

These are all japanese but i feel like japanese movies deliver this indie feel more realisticly 
Check out Alone in Love - it's a drama but it has a very strong slice-of-life/bittersweet indie film vibe. You might also check out the Japanese drama Nobuta wa Produce. The synopsis makes it sound like a typical high school drama, but it has a magical realist strain that is haunting and lovely.
Thank you, Im planning on watching 3-iron, parade, tokyo, backwater, oishii man, kirishima thing, alone in love, and nobuta wa produce. These all look really good to me.

Thank you so much for the recs! I really appreciate it.