Link to original photo on Flickr.
I know Mom did not live there, though. In 1938, she and her sister were living in their first apartment at the Barker Hotel in Westlake.
Here is a contemporaneous linen postcard of the auto rest.
On the reverse of the card it states: "A 67 unit Auto Court with Trailer Sites. Resort Atmosphere in the heart of the City, well known for its Hospitality and Service. Rates Most Reasonable."
Here is an aerial view. As best as I'm able to determine, Mom was posing with her car near the spot where the red arrow is pointing.
Remarkably, Michael Smith, a/k/a Kansas Sebastian on flickr, posted this Then & Now composite of the Silver Lake Auto Court in the 1920s with a comparison shot from 2010. His sleuthing revealed that the older aerial view was taken approximately 11 years before Mother was there posing with her Pontiac.
Click image to view the original photo on Flickr.
Amazing the things one can find on the 'net, eh!