I'm absolutely not into action or political intrigue, but it was City Hunter that got me hooked to k-dramas. I love romance, and it had enough of that to hold my interest. I so think it's a pretty good starter drama, because it has a good mix of genres (therefore can appeal to a wider audience).
Technically my first drama was Hana Yori Dango though, like many other people. I remember finding it addictive but super low-brow and completely ridiculous. I think dramas like that one can be kind of risky though, because many people that aren't introduced to asian culture could be put off by the dynamics of the relationships, that are stereotyped and very different from western ones -- why does holding hands even mean so much? Why are they bickering all the time? Why are they so hung up on a "first love" from their childhood? Do they even kiss, where is the passion, why are they such prudes? Why don't they just talk, and clear the obvious misunderstanding? And the list goes on. Still, I remember being very confused, but enjoying it nonetheless, so it really depends. For me, it was an adventure!
When my friend showed me City Hunter, I was so impressed that a drama could actually have so much quality -- stylish and well written etc. I think City Hunter and dramas that are similar (for example Healer) are actually closer to western movies, so it's less of a shock, and they're suffeciently well-done so that even a person that doesn't have a clue that there's such a thing as asian pop culture, will feel like they're watching something that is sophisticated, and not some obscure show from a strange country :^p