What are some great Korean/Japanese/Taiwanese/Chinese Movies or Dramas that have slice of life and romance elements?  Thanks ^^

If you don't mind older J-dramas I can suggest: Orange Days

Movies:

  • Like for Likes
  • Twenty
  • Sunny
  • Antique Bakery
  • My Sassy Girl
  • No Breathing
  • Seducing Mr. Perfect
  • 100 Days with Mr. Arrogant

K-Dramas:

  • Reply series (1997, 1994, 1988)
  • Because This is My First Life
  • Fight For My Way
  • Suspicious Partner
  • Strong Woman Do Bong Soon
  • Weightlifting Fairy Kim Bok Joo
  • Shopping King Louie
  • Age of Youth 
  • Age of Youth 2
  • Protect the Boss
  • Witch's Romance
  • Jealousy Incarnate
  • She Was Pretty
  • Coffee Prince
  • Drinking Solo
  • The Package
  • Oh My Venus
  • Sassy Go Go
  • My Secret Romance
  • Cheese in the Trap
  • Love Rain
  • Scent of a Woman

Neo covered most of the ones I've seen. In particular, I'll second Because This is My First Life, Fight for My Way, Weightlifting Fairy Kim Bok Joo, Witch's Romance, She Was Pretty, Coffee Prince, Sassy Go Go, My Secret Romance, Jealousy Incarnate, and Suspicious Partner. 

Chinese:

  • Love O2O
  • A Love So Beautiful*

Taiwanese:

  • In Time With You
  • Attention!, Love
  • When I See You Again*

Korean:

  • Go Ho's Starry Night
  • School 2017
  • I Need Romance 3
  • Marriage Contract
  • Madame Antoine
  • To the Beautiful You
  • Dream High
  • You're Beautiful
  • Strongest Deliveryman*
  • Heartstrings*
  • Cinderella and the Four Knights*
  • Heirs*

Japanese:

  • Good Morning Call*

Korean slice of life dramas with a supernatural component (like Strong Woman Do Bong Soon):

  • I Hear Your Voice
  • While You Were Sleeping
  • Another Miss Oh

* These are dramas that I personally didn't love, but that have decent ratings and might appeal to you more than they did to me. My favourites / the ones I recommend the most are in bold. 

Aw, thanks a lot guys! I will watch the ones I haven't ^^

  • Osozaki no Himawari 
  • Sunao ni Narenakute
  • Love Shuffle
  • One more happy ending 
  • Tokyo Bandwagon

Long Vacation (Japan) is a sweet slice-of-life romance.  Alone in Love (by the same writer as Age of Youth) is darker, but has a similar carefully observed slice-of-life feel. Fermentation Family has a complicated overarching plot, but most of the episodes center on everyday interactions at a traditional restaurant, and it has an adorable romance.