Parliament of Victoria
Public visit: Saturday-Sunday (except meeting time) 9:30, 10:30, 11:30, 13:00 (quick visit), 13:30, 14:30, 15:30, 16:00 (fast Visit); Tuesday meeting time 9:30, 10:30, 11:30; another team visit time and meeting time, see http://www.parliament.vic.gov.au/visit/public-tours (Local time)
The Parliament of Victoria is one of the most important unfinished buildings in the history of Australia. Commenced in 1855, it does not have a dome, a northern wing or a southeastern basement, though they were included in the plans. Still, that did not stop Parliament from convening there as it has for over 150 years. You can see how parliamentary democracy works by taking a free, guided tour from 10 AM until 3:45 PM on days that Parliament is not sitting. However, Parliament only has around 50 sitting dates a year, making it likely for you to get a chance to visit.