The building with the turret was the Seymour Apartments at 502 W 1st Street. This photo is dated 3/1/57.
"Seymour Apartments at the corner, fourth and fifth buildings are the Nolen Apartments, 510 West 1st Street, and Beverly Hotel, 512 West 1st Street, respectively."
Huntington Digital Library
Here's a side view dated 2/1/57. The Gladden is just out of shot on the right. It survived a little after the Seymour Apartments.
"Apartments to be demolished; adjacent structure to its south already gone. New courthouse under construction in background across 1st Street."
Huntington Digital Library