Here's my attempt at Penni's Things to do in Melbourne for (almost) Free Meme.
1. Kirsty already mentioned the State Library of Victoria, but I'm going to get specific and mention the SLV's Mirror of the World exhibition. It's in the gallery above the Domed Reading Room, and is all about the history of books and ideas. It's got some very old things (the oldest is a 4000 year old cuniform tablet, plus lots of illuminated manuscripts), some very beautiful things, and some very interesting things. As an added bonus, you can go upstairs to the Changing Face of Victoria, an exhibition on the history of our state, including Ned Kelly's armour, some hair from Bourke and Wills' camel, and Hoddle's chain.
2. The Nicholas building (cnr Swanston and Flinders Lane) is one of my favourite buildings in the city. It was built for Alfred Nicholas in 1926. Nicholas was the guy who reinvented Aspirin after the Nazis "lost" the recipe. The Nicholas building is one of the last buildings in Melbourne to have a real "lift lady" who pulls the lever and makes the lift go up and down*. The Nicholas building is home to many crazy, eccentric artists and workshops, as well as the Victorian Writers Centre, and (my favourite) Buttonmania, home to the best button sale around.
3. The Alfred Nicholas Memorial Garden. Yep, same guy. Very nice fancypants gardens in the Dandenongs. I think there is actually an entry fee, but it's an honour system, so if you are so stumped for cash you can't pony up the $6, I'm sure Alfred won't mind.
4. The Farmer's Market at the Collingwood Children's Farm in Abbotsford. It's $2 for adults and free for kids, which includes a whole day's access to the farm. The market is lovely, and the farm is full of cows and pigs and chickens and horses and other things to pat and smell. It's on the second Saturday of each month.
5. The Abbotsford Convent. Absolutely one of my favourite places in Melbourne. It's right next door to the Children's Farm, so you can absolutely make a day of it. There's a great Sunday Arts Market on the first Sunday of each month, as well as a Shirt and Skirt fashion market at the same time. But mostly it's just lovely to walk around the beautiful gardens, look at the buildings, wander down to the river...
*Eagle-eyed readers will recognise this lift, and the Nicholas Building, in The (Not Quite) Perfect Boyfriend.