I'm traveling to Australia for the first time and I'm going to be in Melbourne for a few days. I want to pack in as much as possible and see all the major sights. What should I go see? What restaurants are a must? What should I experience while I'm there?
If this is your first time in Melbourne, then I think you should visit some of Melbourne's heritage buildings such as the Royal Exhibition building, the Old Treasury building, the Royal Botanic Gardens, Shrine of Remembrance, etc. There are free guided tours and public transport for tourist around the city. Visit the Cooks Cottage, Schwerkolt Cottage, or join in the Night Tours to see Old Melbourne Gaol and step back in time as you explore some old shades of life.
For restaurants, you can easily find everything from Asian cuisine to European dishes around the city central. You should try kangaroo meat, which is one of Australia's specialties. However, if you can spare a day to visit Yarra winery and taste some of the local wine, I'm sure you will find the trip worthwhile.
Melbourne museum is really worth the entire day it takes to look around. For a sports enthusiast, do not miss the Melbourne Cricket Ground and the sports museum. Also, in summer time, one can try the cruises, hot air balloons, helicopter rides. They are once-in-lifetime experiences.
I would suggest a free ride on the tourist tram that take you around the city and docklands. Go for a walk along southbank, on a sunday enjoy the market there and then the ferry to williamstown, have a stroll around there and enjoy the heritage buildings and pop into the information centre to learn more about the area.
For some art, don't forget to check out the National Gallery of Victoria (NGV) as it is was founded in 1861 and is "Australia’s oldest public art gallery." (Quoted from http://www.ngv.vic.gov.au/about-us)
Do note that there are infact 2 buildings:
180 St Kilda Road Melbourne
The Ian Potter Centre: NGV Australia
Another interesting place is the Australian Centre for the Moving Image in Federation Square, Melbourne. It has some of the neatest architecture around!