1. ACMI - The Australian Centre for the Moving Image, located at Federation Square. Screen Worlds is a free permanent exhibition which is lots of fun for the whole family. There are heaps of things to do and touch, video games to play, things to watch and interact with and it's all FREE! There are also paid activities like workshops, movies and other great exhibitions. But you could easily entertain kids in the free area for a whole morning or afternoon (maybe longer).
2. NGV (National Gallery of Victoria), Kids Space. Great exploring (and dare I say learning) opportunities for kids aged 1 - 8. Again lots of stuff to touch and play with. Interactive stars that follow your every move, a sea room with port holes that actually made me feel a little seasick (which was weird - cause we weren't actually moving). There are also the permanent exhibitions on in the NGV which you can take a stroll around and look at (no touchy though - which is hard for little hands). I would totally recommend going to visit the "Never ending illuminated staircase" on level 3. Spooky.
3. Birrarung Marr and Playground, located on the north bank of the Yarra River next to Federation Square. Plenty of space for web climbing, swinging hammocks, tube slides and lots more. A chance to get outside and run (not you - the kids .... well, OK, run if you want to).
4. Melbourne Museum, which is located at Nicholson Street, Carlton Gardens. Which is a bit of a stroll up from the city (or there is plenty of parking underneath). Whilst the Museum is not "technically Free", it's not overly expensive and it is FREE for kids. The thing I love about Museums today is that there are always lots of things to touch and interact with! So it's great for kids. There's everything from butterfly collections and dinosaurs to how the body works and what wierd and wonderful creatures are lurking deep down in the ocean! Think that long toothed fish with the light dangling in front of it from Nemo - only stranger!
5. Now this is technically two in one but I LOVE the fact that you can get a family around Melbourne for FREE!! So if you have never taken a ride with the kids on the FREE brown City Circle Tram (here's the timetable) or the City Tourist Shuttle buses - you are missing out on a treat!! You can get on and off as much as you want and the bus actually stops right next to each of the attractions I have in my top 5 list! Awesome! I can't actually find a link to share with you about the buses - but it stops outside all the main attractions in Melbourne (it has around 13 stops) and it is FREE! (Did I mention that?)
My top 5 are not set out in any particular order or preference - but they are all FREE and we, as a family have visited each one numerous times and continue to go back. So get out there and enjoy some new (and Free) activities.