I find a trip to a local park is always good value. It's free but exciting. Plus you can make it different everytime- take the dog one week, a frisbee the next. Play on the playground or take rollerskates. The park is whatever you and your kids make it.
The Melbourne Zoo. It's such a kid-friendly zoo, not particularly oriented to tourists, but just to anyone who is interested in animals. I really like the relaxed vibe there and the carousel is such a treat!
Melbourne Zoo is amazing. While living in Melbourne when my nieces stayed with me, they loved it. Ice skating at Docklands is also a great choice, as well as Birrarung Maur. Some families still love to take their kids to Luna Park.