At first I was under the impression that I would journey over to Japan's Korean Consulate and get the C3 Visa, or a 90 day tourist visa. But to make sure I inquired with immigration through their petition service online. The response I got was that I can't change my visa to a C3. That was not good news.
So after informing BK and having him call up immigration to get some answers, it turns out I was on the wrong track.
The actual tourist visa I need is the B2 visa which is:
Foreigner who enters Korea without visa for the purpose of tourism or transitThis is made possible by the visa waiver program. The only catch is that this kind of visa only lasts for 30 days. So to extend it all I need to do is walk into immigration and request to extend my visa and pay a small fee.
My journey now is that in order to get this lovely B2 visa I still need to leave the country and come back.
So where should I go? I don't really have all the money to spend several days somewhere, but I am starting to look into it.