Try to find the spot where the photographer was standing.
In case you are wondering where this image was taken, check out the answer posted on Yahoo!7 Answers -
According to parish map 1406150 that I have calibrated against a modern Sydney map, it stood at 33°51'40.13"S, 151°12'24.88"E (WGS84 datum) , close to where the Cahill Expressway loops under the Bradfield Highway.
jbimages got in before me with the map location, however I will post the information that I found when answering the question in Yahoo!7 Answers:
In short, it was on the corner of Gloucester and Little Essex Streets, The Rocks. Unfortunately the building hasn't stood the test of time and was demolished.
"Numbers 140-142 are the remaining pair of a larger contemporary group, now demolished, that fronted Cumberland , Little Essex and Gloucester Streets.
140-142 Cumberland Street is a part of the 'Long's Lane Precinct'. Long's Lane is a cluster of nineteenth and early-twentieth houses, rear yards, and laneways between Gloucester and Cumberland Streets, the Rocks. These buildings are part of the same development as 117-117A Gloucester Street, relating to the NSW Government Housing Board redevelopment of the block bounded by Little Essex (now demolished), Cumberland and Gloucester Streets. Style: Edwardian; Storeys: 2"
The only mention that I can find of the hotel is an extract from an article entitled "Cradle of the Commonwealth" by John Barlow F.I.A. printed in "The Red Funnel" Vol.1. No.1. August 1905, produced by Union Steamship Company of New Zealand. It talks about the peninsula between the present Circular Quay and Darling Harbour, from Argyle Street to Dawes Point, which takes in The Rocks.
"There are still a few residents of The Rocks who remember hearing Wentworth advocate Constitutional Government from the balcony of the old Black Boy - now the Ocean Wave - Hotel at the intersection of Gloucester and Little Essex Streets, though that is nearly seventy years ago."
I also tracked down a photo of Princes Street, between Essex and Little Essex Streets in case you were interested. These buildings were demolished to make way for the Harbour Bridge. This was the same area as the photo on Flickr.
I have also found some other pictures of Gloucester Street around the Long's Lane precinct and have added links for you.
A couple more views of this hotel -