So I'm gonna watch a korean drama with my mum and I don't know what to show her to actually get her into it. She hasn't watched any and this is her first time watching one. I don't think she really likes cheesy cliches like boys over flowers and heirs as much as I do. Any suggestions???
heres some of my favorites (i don't like cheesy love stories too><):

god's gift 14 days
cruel city
reply 1997 & 1988
confession of a murder (it's a movie i made my friends watch it and they really liked it!)
that winter the wind blows
You Who Came from the Stars (super funny!)

Healer might be a good all-in-all introduction to kdramas. In fact, I really recommend you start with that one. 

Something with a bit of fantasy: The Master's Sun

Something serious, but also some sweet moments: Scent of a Woman

Something dark and heavy: Secret
I think it wouldbe best to avoid too young casts so she can still relate to the characters.
I second ViolinGal's suggestion Scent of a Woman for the romance!
Angry Mom would perhaps also bea good choice since it's about a mother & daughter, although it's perhaps too serious. But you might not want to re-watch it all over again :P 

I hope you find something your mother will like :)
What about twenty again? My mom loved it. She could relate to it because she is a stayed home mom and she related to the main lead and liked the flow of the drama. She said it was a drama ( a bit away of reality), but it was nice to watch. Also, she told me she felt less alone, to see that another culture might have the same problems.  She is also liked the male and female lead interactions.
Ah @JPT made a very good suggestion! I think your mum may like Twenty Again. It was a nice show to watch! 
You who came from the stars
Dong yi
Moon Embraces the Sun
Angry Mom.
Second time 20 years old
Mask
Love never forgetting
My sunshine
Queen InHyuns Man
I've watched a lot of dramas with my mum in the room, but the first one she seemed to pay attention to and care about was The Royal Gambler.  She really liked it.  She didn't like Healer *wha????* she did seem interested in Faith, and she laughed a lot at the first few episodes of Oh My Ghost and then stopped watching.
I think moms would definitely enjoy Good Doctor.
Descendants of the Sun, maybe?
moms like historical. my mom does.

Dong yi
queen seon duk
jewel in the palace
empress ki

all the strong females of korean history
a gentlemans dignity
-a good rom com to start with 
Defendant
Dae Jang Geum (Jewel in the Palace)...50+ eps
Flower in Prison...51 Eps.
Remember - War of the Sons