I also agree with Live Up to Your Name. She is a talented doctor who devote her life to do her best at her job, so she hasn't got time for romance. Then she meets the male lead who grabs her attention.
The King 2 Hearts - She is a North Korean solider, and isn't very used to romance and can't find a boyfriend/husband because everyone is afraid of a strong woman. Then she meets a South Korean Prince, and they have a rocky start, but soon they warm up and support each other. Though, one criticism of the heroine, is that she acts cutesy at times. But I think she is very badass character.
And if you don't mind Taiwanese dramas, Autumn's Concerto - Her family's business got bankrupted, and had to succumb to poverty when she was a child, so she had learned how to deal and accept reality as it is. And this mindset will affect how she deals with her life problems and romance later on.
Hi My Sweetheart - it's a romantic-comedy and idol drama. Anyway, the female lead has a bad girl/bully reputation and she shuns everyone. Until she meets the male lead who is pure and naive and she warms up to him.