A Korean female friend of mine once told me that I should never accept an invitation of any kind (even going out for coffee) the first time it's given. She said that I would be perceived as easy prey.
A Korean male friend of mine candidly told me that Korean men relish the chase more than anything else.
This creates a problem of mammoth proportions. If you are a "nice girl" you will be seen as a challenge and let me tell you, Korean men can be relentless in pursuing and wooing their goal. On the other hand, if you go to the movies the first time a guy asks you and you go with him alone, he'll get the wrong idea.
Your best bet is to hang out with a group of friends and not be alone with any one guy unless you are truly serious about him. Be careful about showing or giving too much attention to any one guy. If you are going to flirt, then you'd better flirt with just about guy in your group. Also, watch how you flirt. If you come across as too heavy, you'll scare away the good guys and get stuck with the ones who believe all the Hollywood movies about easy American women.
If one of your favorite guy friends has a girlfriend, you might want to always include her in everything. Korean women can be VERY jealous and you don't want to damage your guy friend's relationship with his girlfriend.