Built for the 1880 International Exhibition, this Victorian edifice in Carlton Gardens symbolises the glory days of 19th-century Melbourne's economic supremacy. It was the first Australian building to fly the country's flag, house an aquarium, hold parliament (in 1901) and receive Unesco World Heritage status (in 2004). Tours of the building leave from the Melbourne Museum at 2pm; call to confirm.
The building and gardens host everything from craft fairs to car shows. While you're there, Carlton Gardens is a stunning place to picnic or rest by the grand fountain, and if visiting in March, you can attend the Melbourne International Flower and Garden Show, the largest in the southern hemisphere, attracting more than 100,000 people over five days.