A friend of mine recommended an English-speaking OB/GYN in Hannam (near Itaewon in Seoul).
I was glad to be able to go before I head home to being unemployed and uninsured indefinitely and wholly unable to afford birth control. By the way, you can stock up on 6 months' worth of the Korean pill for 6,000 won per box. Just ask for 피임약 at the pharmacy. Write it down if you can't say it.
Unfortunately, your lovely teacher's medical insurance doesn't cover any women's health procedures, testing, regular checkups, etc. so it's stupid expensive (over 150,000 KRW) to get your yearly exam done in Korea. But what choice do you have?
The cool thing is that they use mini cameras and/or sonogram to check you out, which is really interesting if you've never seen your own insides before. Or really horrific if you're not expecting it and the doctor says, "Look here," gesturing to the horror flick on a screen you hadn't noticed before. Eep! (They're totally gonna give me copies of the pictures of my cervix along with my records to take home, and I'm totally gonna show 'em around because I need others to share in my shock, too.)
Here's the doctor's Web site:
You can set up an appointment by phone or email, and when you arrive at Yaksu station by subway, give the offices a call and ask them to give directions to your taxi drivers.
My only complaints are that it's really busy and rushed on Saturdays (the only time I can go in since I don't live in Seoul), the staff throws TONS of printed information at you and rushes through explanations of whatever is happening or could happen to your body, and they're REALLY pushy about the Gardasil "cervical cancer vaccine" shot (which has not been tested for whether booster shots will be needed or when, but that's a diatribe for another post, perhaps).
Best of luck. Tell your friends.