Hello~!
As someone who used to be a teenager (ahhh so not used to not calling myself a teen :') ) up until a year ago, I enjoyed a wide variety of genres (as long as they're good, I watch them!) and I had my fair share of school/romance dramas :)
Here are some I personally enjoyed and loved (and some others that were pretty alright but fits your description):
School (High School):
-Angry Mom
-Dream High (Seasons 1-2)
-Monstar
-Page Turner
-Perseverance, Goo Hae Ra
-Playful Kiss
-Reply 1997
-Sassy Go Go
-Boys Over Flowers
-Solomon's Perjury
School (College/University):
-Age of Youth
-Bring it On, Ghost
-Cheese in the Trap
-Heartstrings
-Reply 1994
-Weightlifting Fairy Kim Bok Joo
Non-school, romance dramas:
-Fated to Love You
-Healer
-I Hear Your Voice
-It's Okay, That's Love
-Kill Me, Heal Me
-King2Hearts
-Love in the Moonlight
-Marriage, Not Dating
-Oh My Ghost
-Pinocchio
-Queen In Hyun's Man
-Splash Splash Love
-The Master's Sun
-Shopping King Louis
While this is not a kdrama, I think you would enjoy the Taiwanese movie, Our Times! It is both a school and romance movie :)
Hopefully you can find some dramas you like in the lists! :) Enjoy watching~!