I think it's Ra Ras stalker who will later on cause a conflict of sorts between Jun and Ra Ra and obviously Jun saves her in the end and they live happily ever after.

 AngelOfDestruction:

I think it's Ra Ras stalker who will later on cause a conflict of sorts between Jun and Ra Ra and obviously Jun saves her in the end and they live happily ever after.

i think it will be like this

I  think its dr cha since if you guys saw the piano scene, he was relived since ra ra wasn't playing the piano at night anymore, thanks to the piano she got from dodosol

but the thing is dr cha is too obvious of a guess so maybe its not him since kdramas tend to make it the ones we least suspect?

I think it's going to be the grandfatherly character. We already know he's not what he seems since he acts homeless yet owns Jun's building. His wife loved the piano, so I'm thinking maybe he's her estranged grandfather who kept an eye on her from a distance all these years, attending her recitals in secret.

I think It's Jun . Remember he was preparing himself , wore a suit and everything then he got a call from the grand father . I mean , before that one call , where was he going all dashing with the suit and everything ? 

Its Jun representing his friend who died. Twinkle twinkle little star- stargazing  every time Ra Ra messages DDSSLLS. I think its a reference to someone watchign as a star from above. When Jun met Ra Ra for the first time, it was her graduation performance where she played Twinkle twinkle little star. All of it holds up! I feel like RaRa when she guessed it was Dr.Cha!

I think he could be Dr. Cha based on the fact that he did seem like he wanted to tell her but kept getting interrupted. 

But the stalker is also plausible based on the comment that Classy pointed out.