Checked out The Rock. It used to be a dangerous part of town a hundred years ago but its old brick warehouses got remodeled into expensive restaurants, cafes, and galleries. Some of its alleys are more modern redevelopments that pay less attention to the old style, but it’s still a very nice neighborhood in a very prominent location at the Harbor Bridge. Sydney loves its waterfront and puts promenades, piers, and parks there; unlike, say, Paris or Seattle where they like to close off the waterfront for freeways.
Newtown is another neighborhood, west of the CBD. Its main street is King St, lined with unassuming old buildings with lots of little cafes, restaurants, and second-hand bookstores. But like in many modern cities, the very nice left side of the street is separated from the very nice right side of the street by four lines of heavy traffic.