I came across your post while searching for some historical sites in downtown Atlanta. Mitchell Cargile is referenced with some respect by a reporter for the Atlanta Constitution on 7/19 of 1881 (See "Atlanta and Its Environs" Vol. 2, page 25)
The reference places his undertaking business in a "rear room of the Willingham building". The reporter refers to the "kind-hearted old undertaker" later identified by Franklin Garrett as Mitchell Cargile. I have not been able to find any information on the Willingham Building, but based on this article it was near the NE corner of Decatur and Ivy (now Decatur and Peachtree Center Avenue).
The 1886 Sanborn Fire Insurance map shows the Paris Hotel and the Yancy Building at that location 5 years later, and it is possible that these were once called the Willingham Building, but I can't confirm that.
The reporter goes on to describe this area in unappealing terms. The juke joints house in that building or adjacent to it acquired the names "Ant Hole" and "Beaver Slide" (apparently not the same "Beaver Slide" located near Spellman in the early 1900s). (For more on the former, check out http://www.earlyblues.com/essay_peg%20leg%20howell.htm
I hope this is helpful.