Perth Cultural Centre (Museum, galleries and State Library) offers loads of free fun activities for children. Otherwise, Kings Park has plenty to entertain little ones for the whole day as well as beautiful shady spots, just perfect for a picnic. Maylands Water Park, down near the Swan River, is popular in the hot weather and has special pools for babies and toddlers.
Finally, if it's not too hot, a great way to keep children happy all day is to take them to one of our beautiful national parks. John Forest, Beelu, Serpentine,Yanchep and Walyunga are some of my favourites, but there are quite a few others. All have plenty of walking trails and if your kids love native animals you're almost certain to see kangaroos, especially in the late afternoon. All these places have picnic areas so you can easily spend an entire day close to nature.