Australian National Botanical Gardens- great for picnics, checking out plants and letting the kids burn their energy off! There's a cafe, story time on the first Friday of the month and art and craft activities throughout the year.
Tidbinbilla Nature Reserve - too many things to list! Amazing adventure playground, walking trails, wetlands to explore, ranger guided activities including meeting platypuses and koalas, soooo many things to do here!
Canberra Reptile Sanctuary - all indoors and smaller than I expected, but the kids love it and it's located at Gold Creek which has loads of cafes, shops and other tourist attractions for kids and adults alike.