ratcharge
Hey man! Bummed you're gonna be there when I'm in Italy, but hope you have a blast..
Loads of stuff to do in Melbourne to your tastes.. Cafe Gummo is a great anarchist bar who do gigs. Spit in Footscray is a sick DIY space, really great people run it. Bell City Tavern is also a great venue for gigs, DIY and on the downlow (the entrance is hard to find but loiter around and follow someone in). Those are my favourite spots at least. Essentially all the pubs are really good.. the Tramway does shows and is a nice place to hang out on a winter afternoon, and it's not too far from the Queen Vic markets which are a good place to get lunch. The Tote is the "iconic" pub venue and definitely worth going to for a beer or to see a show.
This gig guide is pretty reliable to check out for actual events: https://melbourne.askapunk.net/
If you're there on a Sunday the Coburg Trash & Treasure is meant to be a great flea market for finding cool things. The ACMI museum (for cinema/TV) is really cool and there's lots of good archived stuff to watch in there. I'm not sure about other museums and galleries and the like to be honest, but for Indigenous culture the Garry Foley collection at Victoria Uni has a good slice of digital content online to browse through ahead of time.
Shops for zines and books and stuff I'm not sure of these days, Rowdys Records has a good range though to get started and I'm sure they'd be able to point you in the right direction. At the very least the street that's on you can just walk along and find cool stuff as you head towards the city.
As for Tasmania! I haven't been since 2015 and a lot of their venues have closed, but it's a really really small city so you'll no doubt stumble on whatever's there. I can't remember names of anything but I remember really liking the harbour and the pubs down there at least!
Have a fun trip mate! Make sure to drink VB (best beer in the world), drink a flat white, eat a good quality meat pie, a chicken parmigiana at a pub, and you'll have more or less experienced the entirety of the "Australian" contribution to food haha. Hope it all goes well 🙂