OK, I'll try to tell you about what I love about Melbourne. That's where I live. I won't go on about touristy things & "must sees & dos" because you can read that sort of stuff anywhere. And really, if you're into the spectacular touristy things, well, the city of Melbourne might not be first on your Oz travel list!
I see Melbourne as a big, sprawling collection of villages, really. There are parts I never go to because it's a helluva trip to go from one side to the other. And you need a good reason to do this, to put up with all that time stuck in your car! So I'll just talk about the bits I know & like & often frequent. I love the city centre, changing all the time & now so often full of visitors, whether for some sports event, tourists & backpackers, or just visitors from the suburbs. I love the trip to & from the city: you always meet interesting people, usually asking for directions, or just wanting a chat.

My usual purpose for a city visit is to visit the (wonderful!) art gallery (NGV) to catch up with a new exhibition, to meet friends & eat (great cafes!) to attend a political rally (often!

), or for else some particular appointment.
But my very favourite thing about Melbourne, is our mad passion for politics & ideas. We take this stuff
very seriously! We bicker over politics & current "issues" in our daily newspapers, in our workplaces & while shopping! We hit the streets in huge numbers on just about any political issue you can name. We thrive on argument & a good cause!
But the parts of Melbourne I know & love best are where I live & my regular stomping grounds that radiate from there. My bit is the inner north. I just love it here! It's very "melting pot", definitely not "salubrious" or "establishment money"

& changing all the time. (Apart from very established suburbs like Carlton, which is now unaffordable & full of doctors, lawyers, architects, etc, etc.) But once you're out of Nth Carlton it's a whole different story: suburbs traditionally full of migrants, students, first home buyers & now the "trendies", too.
To give you some idea of my home turf, let me tell you about where I usually shop. This is all in the next block from my street, a 5 minute walk: My hair is cut by an overly-exuberant young, groovy Greek fellow

, at the 2 middle eastern shops I buy my dried lentils & beans, I buy my coffee, fruit vegies & cheeses at the market, generally from Greek stall holders, my bread rolls from the Vietnamese bakeries (both shops run by women), my spices & other cooking bits & pieces from the Indian shop (the young man from Hyderabad could sell anything to anyone, I swear!

), a Chinese herbalist's shop is intriguing with his pills & concoctions for every known ailment, the Turkish kebab shop sometimes tempts me when I'm too tired or too lazy to cook dinner (as do the Egyptian, Indian, Himalayan cafes & the Egyptian felafel shop, the middle eastern cafes, the Asian noodle shops, etc.). I'm expecting that soon we'll also have some African shops. They're the newest wave of migrants & very visible on the streets. Sometimes I sit outside at one of the (usually Italian) coffee shops & just watch the passing parade. Folk from just about every nation in the world pass by. To me it's just fascinating!