Here is some reccomendations from YT:

Well, asian drama always wanted to promote romance drama, because it is an important subject things to overseas and non-asian fans of romance.

And if you are willing to watch non-Romance asian dramas, you'll have to watch it through illegal streaming websites.

Solomon's Perjury (My favorite kdrama)

Cross

Nightmare Teacher

The Legendary Lackey (Drama Special)

Dramas that have slight romance, but are more comedy focused:

We Are Peaceful Brothers

Go Go Waikiki

I'll throw in 2 Thai dramas as well:

Project S: Skate Our Souls (The only drama I've seen to make me cry, but very good)

Project S: Side By Side