Places I have enjoyed:
1. Eureka Skydeck - It is amazing, to see every aspect of Melbourne from the tallest building and if you are daring enough walk out onto the glass floor 100 floors high!
2. Free city tram - Melbourne is known for trams and this tram is the oldest in melbourne and free, it is purple/marone and takes you right around the CBD of Melbourne, it tells you where you are and facts about the places the tram passes.
3. MCG - Watch a game of football or cricket at the Melbourne Cricket Ground
4. Visit the alleyways in Melbourne that are full of artistic restraints and pubs (google where to find some, I can't explain any.)
5. Go shopping at DFO - Direct Factory Outlets, Melbourne has 3.
6. Visit Geelong - The second biggest city in Victoria, it has great views and a great vibe.
7. Visit any of the art galleries. Most of them have free sections.
8. Visit a beach (Don't know the name, you should be able to find it on Google. It is famous for the people of Melbourne.). This particular beach overlooks the Melbourne skyline, it is beautiful!
9. Visit docklands, it is amazing and has great restraints and great views.
10. Visit one of the many theatres for a performance. (Most of the theatres are near the China Town district, it is the oldest China Town in the world.)
11. Visit Luna Park - A theme park, it is pretty lame but the only one in Victoria. And it is in the city.
12. Visit Sovereign Hill, it is ages away from Melbourne but it is worth it, it really does take you back 100 years to the gold rush of Victoria! It is a great place to visit.
This is all I have. :)