To be honest, the best qualifications to have in Korea are
1) To be young.
2) To be female.
Your TEFL doesn't mean much, especially if it's an online TEFL (I would even go on to say it's sort of worthless myself unless it actually included a few hours of observed teaching, meaning the tutor observed YOU teaching).
Having said that, if you have a good GPA, you might want to consider signing up with SMOE. If you tell them about your TEFL (even if it's an online one) you might be able to later on, get a pay raise. There is only one recruiter for SMOE (
www.koreaconnections.net ) Also, I have a friend that is a head teacher in one of the Seoul districts.
I would however recommend against Seoul mainly because Korea has much to offer that you will hardly ever get to see. Merely because it's a real pain to leave Seoul to go see something and then coming back to Seoul is a real pain. Think, trying to leave New York City to go visit Woodstock and coming back to New York City when you are done and multiply all of the traffic problems by 3 or 4 and you will get an idea of what I am saying.
Also, Seoul compared to both New York City and Tokyo is quite drab in my opinion. Not really that much variety in architecture (although this is improving), very few decent parks (unlike Tokyo), no seaside areas, ... It's pretty much the same boxy buildings with a little bit of mountain scenery here and there. Pretty much the only thing Seoul has going for it in my opinion is, whatever you are looking for culturally, if it's not in Seoul it's not in Korea (unless you are talking about old traditional culture). But as far as a variety of scenery? Seoul doesn't have it. A place that's quiet where you can relax? Seoul doesn't have it. Keep in mind when I say "Seoul doesn't have it." for those two I am thinking in my mind "compared to other places IN KOREA". For example, if you want a good beach, there aren't any in Seoul but there are in Gangneung, Wondo, Pusan, ... you get the picture.
Seoul also has the added disadvantage that too many people want to go there, meaning that getting a job there will be more difficult for a city that is kind of over-rated.