The Old Treasury Museum (building) completed in 1862. It is considered one of Australia's finest Renaissance Revival buildings. It was constructed in Palazzo form from wealth generated during the Victorian Gold Rush. It's purpose was to house the state gold vaults. It hosts daily tours popular with tourists and students.
I've personally took the kids last year and learned more than I thought I would. The kids were a little bored so they demanded my phone to play games on half way through. Also see the Treasury Building.
Car parking is available on the street. If you rent a car or drive, there is plenty of parking near by.
There's also public transport options.
Trams 11, 42, 48, 109, 112 and the free City Circle Tram stop near the Old Treasury Building Train Train to Parliament Station
Keep up the fitness and walk! Check out the map