If you are in Hyde Park, Sydney on a weekend near the Archibald Fountain you are almost sure to see the bubble man - he gets a huge crowd as he send bubbles flying and kids race after thhem. So much fun to watch. When we are in that neck of the woods the kids beg us to see the bubble man.
NSW Art Gallery - free entry except for major exhibitions. Ask for a kid's trail map at reception and the kids will have fun searching out works of art. An easy walk from the Sydney CBD through the Domain, a green open space.
Sea Life Sydney Aquarium at Darling Harbour, Sydney, is a pure delight. Get there early on a weekday if possible and you may have the place almost to yourself. Take a snack to eat at the end of the aquarium where there is an enormous window - sit for as long as you like and watch the fish.