So you want a romance without melodrama? do you want a comedy? thriller? can the romance be true but secondary to the story?
I'll suggest the following from my favourite dramas because I think they're well drawn relationships that focus on characters
Healer - It's a mystery/crime/corruption story but the romance is wonderful and not the main story
Faith - Fantasy/Historical. There's a lot of ridiculous shenanigans kidnappings, poisoning etc but it has pretty much the best relationship I've ever seen between the main characters; communication, cooperation, no love triangles. there is a bad guy but he's flawed and you understand at each turn why he does what he does
Fated to Love You - although the 2 middle episodes made me cry my eyes out, in this drama there's some fantasy (animated snails, the ability to freeze or burn, crazy eye makeup depending on characters' moods, a silly laugh) there IS NO BAD GUY - this is super rare. Although there's a bit of heartbreak, I do think there's enough comic relief to make up for it.
Reply 1998 - No drama, no bad guy. just slice of life and good relationships - it's long though, episodes are 1 hour 20 minutes and there's 20 of them.
Reply 1997 (I haven't seen 1994 yet) again simple, well told relationships. I found elements of the "mystery" in this removed focus from the story but make of that what you will
You're All Surrounded - Crime and true love. Really great character development. Interesting plot. the romance is not the focus but early on I didn't like the female lead but by episode 6 I cared about her so much and I wanted everyone to be happy. Plot twists in this made me gasp.
Coffee Prince - again NO BAD GUY just people fighting their own preconceived ideas of love, with lots of support from people who love them
Baek Hee Has Returned - Older Leads separated in their youth: hilarious and only 4 episodes - an easy emotional (in a good way) watch
I've taken a bit of a licence here, some of them have a fair amount of drama, but that's only because I don't quite understand what your idea of drama is. In the ones I've suggested there's no "Evil Mother In Law" or no one who wants to keep the lovers separated for no apparent (or a totally ridiculous) reason. There's also no endless crying by the actors (something i really really hate - it makes me feel less for them). Another thing I'm not a fan of is "Noble Idiocy" by that I mean "I'm gonna break up with you because I think I'm bad for you, I really love you but I'm gonna pretend I hate you because I want you to have a good life and not think of me" There is an element of that in Fated to Love you, but I give it a pass because I find the reason sufficient to the story. Of course all of this is entirely subjective :)
