Hey there...I'm not from Melbourne myself, but I live close by and try to visit the city at least once a month. One place I always make sure to visit is Harbour Town. It's just a great place to shop - there's like 90 different stores if I remember correctly.
And if you want to visit a place where you can take great pictures, I'd definitely recommend is the 12 Apostles, located at Port Campbell National Park. I swear they're breathtaking and anyone you show the pictures to will be instantly jealous!
I hope this helped. You could also just try googling "best places to visit in Melbourne" and I'm sure you'd find a great list!
Within Melbourne City you can see South Bank, Hosier Lane, Federation Square, Flinders Street Station, and you should visit the city's laneways. Outside the city, you can visit the Great Ocean Road, the Great Otway National Park, as well at Grampians National Park. In fact, you could road trip with a camper van and do both over the course of a week.
I would recommend the following places in and around Melbourne;
- Yarra Valley and Ranges
- Dandenong Ranges
- Mornington Peninsula (including the wineries and the hot springs)
- Philip Island & The Penguin Parade
- Queen Vic Markets
- Banksy Art Exib is currently still on.
These are just a few things the tip of the iceberg really!
I would also add to take a look at what sport is on when you visit ... we are a huge sporting city!
You don't really need to go outside the city and inner suburbs. I'd say explore the CBD, see all the nice shopping centres and try out a few places to eat. Then makre your way over to Chapel St in Windsor/Prahran and check out the nightlife, always fun and enjoyable with many great places to eat too. Brighton Beach is good for a quick stop by if you do not want to be driving out far to the Ranges or Yarra Valley.