Purple Wyrm: What!?! Minotaur Books is still going? It's wonderful, or was when last I was there. Unless it is much changed, well worth a visit.
Owl: Minotaur, as mentioned. They used to be in Swanston Street, but I think are now in Flinders Street? Also: the State Library in Swanston Street - worth going just to look up at the dome from inside the Reading Room, which is a treasure in itself, harking back to English library reading rooms of the early to mid 1800s. And the Lilydale marble in the foyer has graptolite fossils. The Museum, same area. Back when I lived in Melbourne, the Art Gallery was there too, but now it has moved from the old goldrush-era stone buildings to a modern one on the other side of Princes Bridge. Still amazing collections though, and Princes Bridge itself is worth a look if you like curious old things.
Also up the Museum end of town, see Chinatown in Little Bourke Street. Eat at the Kun Ming, which is no longer the fan-tan den it was in my day, but still serves amazing food, and if you're sensitive to food chemicals, I've never had a bad reaction from anything they served, and they are not insanely expensive. Chinatown is mostly Little Bourke and Little Lonsdale Streets, and the old cobbled lanes in between. Go and see the cobbled back alleys where some of the Phryne Fisher tales were filmed.
Off Collins Street is the Block Arcade. Beautiful mosaic floors, interesting architecture and little shops. Stand in the middle of the arcade, look up and see Gog and Magog, statues of Giants out of English Folklore. Imagine the place about a hundred and sixty years ago, when 'taking a turn around the Block' was the fashionable promenade for upperclass twits.
See the Shrine of Remembrance on St Kilda Road, with Kipling's poem inscribed around it. There's a sculpture park between the Shrine and the Myer Music Bowl, which itself is worth a look, and if you keep walking east from there you will find the Melbourne Botanic Gardens, which are a treasure in and of themselves, and have lots of shady cool spots even on stinking hot days. Sadly, the old tea rooms are gone, but the lake is lovely, with black swans.
Have high tea at the Windsor Hotel in Spring Street, then walk across to the Treasury Gardens to see the old conservatory, and possums in the trees (though maybe you've seen enough possums yourself?). Also the Exhibition Buildings, Ola Cohn's Fairy Tree, Captain Cook's Cottage (yes, the original), and the Miniature Village.
If you like steam trains, go up to Ferntree Gully and see Puffing Billy (though you can't ride it in summer, I think, because fire bans).
Anyway, that's a few of the things you can do in Melbourne, before you even get to the suburbs (or under the city, where are all these lovely brick-faced early nineteenth century tunnels and storm drains, or out to Carlton where Lygon Street has the best coffee, and Drummond Street has an old house with kangaroo/dragon gargoyles on the roof, and........)