I also heard quoi. But, because I don't have a great ear for languages, I often go to Google Translate (after the fact) to see if I can hear differences there. And this time I found that coin has a more nasal sound than quoi: https://translate.google.com/#fr/en/coin%2C%20quoi
"un" = "a(n)" "le" = "the". "Dans le coin" would be "around here", as in "Il vit dans le coin" = "He lives around here". It is an idiom and a handy one at that. Another similar one: "je ne suis pas du coin" = I'm not from around here. http://www.larousse.com/en/dictionaries/french-english/coin/16908
It's not "in the corner", but "in a corner", although either makes perfect sense.
A corner is not a rare thing. Unless you have been to the Oval Office, then probably every room you have ever walked into has at least eight of them.
But I'm afraid you strike me as the kind of person who would think there were only four.