I'm staying in a Guest House near Hanyang University in Wangsimni. It's pretty nice room. A little small, but there's a sturdy bed, TV, closet space, mini fridge, free wireless, a passcode entry and a communal bathroom.
The neighborhood is pretty quiet, but quite close to the University. I think it's a pretty safe neighborhood; there's a police station just down the street. You can hear the train go by, but maybe that's my room location. The guest house is right off the train tracks here, so if you're a light sleeper...bring ear plugs.
The owner is very friendly and kind. In fact his English is great! I didn't have any problems getting checked in or finding amenities. He was thorough and gave me his cell phone number in case I had problems.
I'm kind of tired now though, so I'm not going out again until tomorrow.