I like to give my son one of my old cameras and take him out for a photo shoot - this can be a beach, park or even the backyard. He takes photos from angles that I would never consider and his photos usually turn out amazing.
Our State Library has a children's corner which is open every day of the week. It is adjacent to the State Museum which also has free admission. Add the nearby art galleries and you have free activities to keep young folk occupied for hours on end.
Some great, totally free, activities to do with kids include visiting the library, going for a bike ride together, visiting a local national park (for a picnic and bushwalking) and teaching them how to cook at home.