She has never watched dramas before and want her to watch one with me while I visit her.
Really want an amazing drama to show her!

-Good plot, doesn't get boring (this is really the biggest thing for me)
-NO sex scenes lol
-Romance/comedy is good, but can be other (just no thriller)
-Want Kdrama, but doesn't have to be
-Easy to find online (Viki, dramacrazy...)
-Can be one on my list

I keep thinking of dramas I have watched, but it's just hard to pick one.
You could start her of with a classic - Winter Sonata (My first ever Kdrama which got me hooked) If you haven't seen it then you could both watch it together.
I watched New tales of gisaeng with my mom and now we're watching King of dramas :D
Jewel In The Palace and Brilliant Legacy...my mom loves them ^^...
the rules are simple...they have to be educative with lots of struggle and hard working or revolve around family and ethics...these kind of dramas make you look good in front of your mother and she will love them "because they teach you something"...don't pick up something violent or with lots of romance "they make you look silly" xD
...and more recommendations :D

Saranghae / http://mydramalist.com/korean-drama/1185/saranghae#c206538 /

This drama is really about love and life.
Good acting, good storytelling, slice of life mixed with some romcom.
First drama where i didnt get annoyed by manga references or jokes, ok, sometimes it was tiny bit too corny but i managed survive. Soundtrack...normal i think. I recommend it, give it a try.

p.s. I think it is watchable for guys too bc a lot of story is told from male perspective.
Hmmm, I watched some dramas with my grandmother like Jewel in the Palce, Stars falling from The Sky and My name is Kim Sam Soon so maybe your mother would like them too.
I really recommend watching History of the Salary man! Both me and my mom loved it! :D It has basically all genres mixed, very interesting, smart and complex storyline, superb acting, has romance and is extremely funny!
Dong Yi (this historical with good storyline).