I'm from Brisbane so we are fortunate to have many wonderful family friendly destinations close by. My top pick, though, would be Southbank for the beach (beach type lagoon), Science Museum, family friendly restaurants, markets, Gallery of Modern Art, State Library of Queensland, Maritime Museum, BBQ and many park areas.
Brisbane CBD is right across the river from Southbank, so a walk across a bridge or a ferry ride on one of the many CityCats could be part of the adventure. There are often many activities for children and families happening in Southbank and the CBD. Southbank really offers so much that can't just be all done in one day. There are many family friendly accommodation spots in and around Southbank.