When I visited Melbourne last year I went to the State Library, initially just for the free WiFi. Upon entering, I was totally blown away by the magnificence of the architecture. It's absolutely spectacular - pure post-Gold Rush, high Victorian era magnificence. The dome above the reading room was spectacular, and I spent a few very satisfying hours wandering around, admiring the architecture, the art and checking out the various historical exhibitions. I strongly recommend a visit to anyone visiting Melbourne and locals who haven't yet been.
Iím from Sydney, but I did visit the wonderful Melbourne State Library for an exhibition & the cafe afterwards, about 6 years ago, & Iíd love to go back there, but havenít got around it. I am in Melbourne 4 or 3 or 4 times a year, visiting family.