I spent most of the last week at the State Library of Victoria. It's a grand old pile, built in the 1850s when Melbourne was awash with gold money (apparently, it was one of the richest cities in the British Empire). For the last decade or so, it has been undergoing works of some kind -- first of all to refurbish and expand the whole building, for the last few months they have been doing something at the offsite storage area which means that all the old journals like Fortnightly Review and Nineteenth Century and After are unavailable until after Easter (ie this weekend, finally!)
I'm sure it's not a patch on, say, the old British Library Reading Room, but the La Trobe Reading Room (above and below) is a rather nice place to sit, read and write. (There's another big reading room, but La Trobe is nicer and quieter.) It was opened in 1913 and is covered by what was apparently the biggest reinforced concrete dome in the world. Well, it is big, certainly. It also has a big collection, 1.5 million books, and I'm always surprised at (and grateful for) the amount of primary source material I can find there. Any time I look up some musty old 1920s book on airpower by J. M. Spaight, say, or "Neon", there must be at least an 80% chance that the SLV has it. (If it's non-fiction, anyway -- 'works of fiction and of the imagination' were specifically excluded back then.) They are not so great on British newspapers, but you can't have everything ...
To me though, this building will always "really" be the Museum of Victoria, which shared the building up until the mid-1990s -- in fact, I'm not sure I even knew there was a library in there as well, until the museum moved out! I loved the rabbit warren that was the old museum, and visited it many times. I even worked there for a few months as an "Explainer". It's great to have a swish space for the all the library's collections, but I do miss turning around a corner and bumping into a mummy or a racing horse, or even a musty old set of dioramas illustrating the history of warfare, which must have themselves dated to the interwar period. The new Melbourne Museum is great, but lacks the charm (and the dioramas!) of the old museum.
PS The photos on the Wikipedia page are much nicer than mine, so go look at them too :)