This painting by Julian Ashton appears to be from the west end of Argyle Street in The Rocks, facing south-east towards Observatory Hill, near the corner of Windmill Street. 

Despite repeated threats of demolition during the 20th century, Argyle Street still retains many of its historic buildings. The Lord Nelson Brewery Hotel, constructed in 1835, stands at the corner of Kent Street, close to where Ashton must have been standing to paint this scene. From this vantage point you can just see the time ball and weathervane of the Sydney Observatory tower, emerging from behind the trees.