Does the Soul Society know exactly where Kisuke Urahara is? I was under the impression that Kisuke's shop is where it is in order to stay out of the eyes of the Soul Society. Yet during the start of Season 4, Renji is "mooching" off the Urahara Shop, and it doesn't seem like Renji was in need to help at any time which would lead to Kisuke offering help, unlike with Rukia where it was shown that after she lost her powers she was approached by Kisuke.

So I am wondering if the Soul Society knew that Kisuke was set up in Karakura Town and thus directed Renji to seek his aid. If not, then how did Renji end up there?
The simple answer?  Yes.  However, the arc you are speaking of does not exist in canon.  It was a filler arc.

Now, to expand upon the actual answer to your question.  The Gotei 13 does know where he is, in-fact, they even know where his shop is.  The reason they don't arrest or execute him is because he is still a useful asset to them.  Now, if he was useless or ended up causing too much trouble, they would likely dispose of him, especially after he helped Ichigo and the others to gain entrance into the Seretei (sorry if I misspelled that).