I second My Mister: It is a very heartwarming and realistic series. Not enough words to describe it. If you like realistic dramas, with character-driver stories you will love it. Personally it is my favorite series of all time.
Children of Nobody: Since you liked nobody knows, I am almost 100% sure you will also like this one. This series deals with a very sensitive subject (child abuse) in a realistic way without being over-dramatic and without making the viewer cry every few seconds. It deals with a a lot of different things, but for me what made it a masterpiece was the fact that there are many moral dilemmas.
The Nokdu Flower: In my opinion this is one of the most underrated historical dramas. It has a great cast and it deals with a real historical event. It is a very inspiring story that doesn't sugar coat anything.
Six Flying Dragons: Frankly, this drama doesn't start that strong. It is very complicated in the beginning especially for someone that hasn't watched any korean historical dramas before. However, it gets interesting as it progresses. All of the characters are memorable, there are some amazing fight scenes, that you rarely see in a kdrama and Yoo Ah In is beyond phenomenal.
Hot Stove League: This is a really nice and heart-warming drama with fantastic performances. It deals with the preparation period of a baseball team. As a person that lives in a country that baseball is not well known (I doubt if there are any baseball clubs at all) I found it peculiar that I enjoyed it that much.
SKY Castle: Since I am being honest, this series doesn't start as strong as someone may think. It takes about 5 episodes to get into it, but after that it is simply great. It deals with the educational system in Korea. It is quite raw and heart-breaking. It has a fantastic direction and every actor is amazing. It is binge-worthy after the first 5 episodes.