I'm a wine professional, living in Bangkok and travelling frequently throughout South East Asia. I'm a huge fan of Laos and Cambodia and off the beaten track travel. Feel free to contact me at: www.facebook.com/mil.elephants
Melbourne is not cheap. I know I'm stating the obvious, but it's become less and less affordable over the past few years and for someone like me who normally resides in third world Asia (not Singapore or Japan) it can be a big shock to see how much the cost of living has risen in the past decade in Australia.
That said, there are a few ways to economise that won't spoil the enjoyment of your stay.
Accommodation can be a major expense and for the cost of a shared room in a hostel (with no private bathroom) in Melbourne, you can stay in a four star hotel in Bangkok or Kuala Lumpur. For groups of people four share rooms in hostels are an option but they are still basic. Apartments, again for groups can be a good option. Airbnb is also worth trying, and somewhere just outside of the CBD can be good value. Always check the comments for tips on how easily you can get in and out of the city.
Meals can also be quite a shock, especially for families. My favourite remedy to this is to head to the Queen Victoria Market and buy provisions for a picnic. The food is stupendous and with such variety, any tastes are catered for. It's also quite possible to cook a barbecue. Meat in a Park is perfect for finding a BBQ when you need one.
Many restaurants have great specials, and lunchtimes tend to be cheaper. Serving sizes may be smaller at lunchtime, but really, do we need servings to be larger in Australia?
Transport, well that one is easy, at least inside the CBD. Trams are free and you should use them liberally. Just be careful to look for the green Free Tram Sign on the stop to make sure you're not going to get caught out without a ticket.
There are plenty of free activities in Melbourne, and here are a few of my favourites. Melbourne is actually full of freebies. You'll also find travel agents and ticket agents often have discounted tickets for popular destinations such as the Aquarium and the Penguin Parade.
For those of you who like a tipple, there are lots of places in the city offering happy hours, mostly during the week for city workers. If this is up your alley, Network Bar and Pizzeria at Southern Cross Station is just about the cheapest place I've found.
All in all, Melbourne is a great place to visit, and there are many ways to economise so that you get the most out of your trip.