"You were correct about the large institutional building at the Klotter Park. It was the location for the old 28th District School.Built in 1880 with an addition in 1887. There is a book "A History Of The Schools Of Cincinnati" by John Brough Shotwell.Look it up on Google books. It has a pic on pg 308. It was on Browne St.(guess it was a street back then,not an alley) west of Baymiller."
So I looked up the book, and for the public record here is the sketch and description:
And here is a Sanborn Map showing the School:





