I have converted 3 people (and possibly 4) with You're Beautiful. Be sure to tell your friends be open-minded and give it a chance!
My Girlfriend is a Gumiho is pretty easy to watch and understand imo. Great and simple romcom with two of the most talented and beautiful actors in South Korea atm.
I did it with The Greatest Love.. but Personal Taste should work too.
I have only got one person converted, and not totally at that, but he's weird and he's my husband. It started with him watching the variety show Running Man secretly while I was watching and laughing out loud. But, the first drama that garnered any attention from him was the K-drama Que Sera Sera, to his Western mind it didn't seem to odd or out of place. After that he was kind of blah, so I started watching a Historical drama called Queen Seun Deuk (I don't think I spelled that right), he watched it in its entirety with me, followed by watching all the Running Man episodes and the drama A Tree with Deep Roots(he watched this in a weekend). Now he is watching movies on the Asian Crush channel on the Roku. I would suggest a variety first, and depending on the age of the other person, Que Sera Sera.
Well my first drama was You're Beautiful and I loved it (but i have had lots of experience to manga and anime, though Asian dramas were completely new to me). Others I think that should be watch while still a drama newbie are: Boys Over Flowers, Hana Kimi, Heartstrings, Playful Kiss, Flower Boy Ramyun Shop (totally need to get them into the Flower Boy series haha), Personal Taste, and Panda and Hedgehog. Maybe Full House as well, but there is a lot of cleaning and arguing to put up with though still a good drama. These are ones I watched while I was new/ish to dramas.
you're beautiful? or kimi wa petto or maybe a live-action movie like high school debut (was the self-conversion point for me, cause i loved the manga) or paradise kiss