One of my favorites is You're Beautiful. Many people would recommend this. It stars Park Shin Hye, Jang Geun Suk. Jung Yong Hwa and Lee Hong Ki. It's about a girl who pretends to be her brother and joins a very popular band A.N.Jell. It has many funny parts, a few sad but is so cute and enjoyable!
Another one I love is Shining Inheritance/ Brilliant Legacy. In this drama the female lead gets offered the large inheritance from a random old lady she helped instead of the lady's family. The acting in this drama is amazing. There is an autistic kid in it and you could actually believe he is autistic (the actor).
One I didn't have many expectations of but ended up loving is The King 2 Hearts. It features a lot on the troubles of North and South Korea. The acting is also brilliant in this drama and it's so intense. There is so much suspense and you don't know what will happen next. I love the romance in this one too.
Some more I would recommend are:
Stars falling from the sky; very annoying female lead at first, but she matures up and it turns into a great drama!
Goong (Princess Hours); female lead is forced to marry into the palace with a cold unemotional prince.
Mary Stayed out all Night; Also stars Geun Suk, his character keeps getting pulled into Mae Ri's troubles.
You could also try Dream High 2, but I've heard it's no where good as the first one.
If you like You're Beautiful, K-Pop Extreme Survival is very similar.
Flower Boy Ramyun Shop and Oh! My Lady are both really good dramas.
I hope you like these suggestions. :)