
The first burials of Europeans after 1788 in Sydney took place near the shore presumably near the hospital in George Street. It is only conjecture but Ruth Park makes a good case for the area shown in the photo.
Looking from Campbell’s Cove.
“Pause a moment and look towards the west. Somewhere here, between Metcalfe Bond and Gloucester Walk is the probable site of Sydney’s first graveyard. This place at the Rocks in all likelihood was Sydney’s first graveyard, where some of the sick of the First Fleet, for whose care Captain Phillip hurried up his portable canvas hospital, found their lonely resting place. Others say that the first dead were buried up close to the ridge, where Harrington Street now is, but it seems unlikely that graves were dug in so rocky and so precipitous a place. Here, in a patch of sandy earth, in this bay so like hundreds of others still around Sydney, a cranny of glistening cutty-grass and sparkling sea, a bay convenient to the hospital and yet some distance from the marine and convict camps - here they surely laid the forty-one exiles, including ten children , who died in the settlement’s first five months.”
Ruth Park

Part of Taphophile Tragic's to view the others click
here.