There is Guillaume at Bennelong within the Opera House itself, Opera Bar in the Lower Concourse, Bistro Mozart in the box office foyer, Sidewalk Cafe and Bar and various theatre bars.
There is a whole row of indoor/outdoor restaurants on the approach to the Sydney Opera House from Circular Quay along East Circular Quay.
On the other side of Sydney Cove are a number of restaurant and bars at the Overseas Passenger Terminal and within its vicinity at The Rocks. All are within comfortable walking distance.

