When we lived in Adelaide's CBD in the first decade and half of the 21st century one of my favourite afternoon poodlewalks was in Adelaide's west parklands, especially Park 23 (G.S. Kingston Park or Wirrarninthi) with its sculpture trail plus the heritage listed West Terrace Cemetery. Wirraninthi used to be called Wirranendi, and over the years that I was living in the CBD I witnessed its extensive replanting with trees, shrubs, grasses and the ecological rehabilitation of the stormwater wetlands.
We--the two poodles and me-- would spend many an hour wandering around and exploring the cemetery in the late afternoon. It was safe territory. The poodles could explore the fenced grounds whilst I could take photos. I just had to keep an eye out for the cyclists riding through the grounds and for the occasional graveyard visitor. I usually went to the forgotten, rundown areas, which I found more to be more interesting than the newer, and more flashy Italian/Greek grave stones. I thought that the latter were excessive--over way the top.
I would usually park the car in the small car park off Sir Donald Bradman Drive, walk west towards to the railway line, turn south past the fire sculpture, walk along the path adjacent to the railway and the wetlands, then walk east around the corner with its wind sculpture, and finally into the cemetery via the gates on the Catholic Cemetery Rd.