Australia is expensive now, but Sydney is about 10% more expensive than Melbourne across the board. I've lived in both cities and loved Sydney in the mid-nineties, but the money has ruined everything except the parks and beaches.
Fortunately you can find plenty of places in Melbourne that you can enjoy on a budget. We were staying with friends in Carnegie (the illustration above shows the fancy new elevated train station). The suburb is only 20 minutes on the train from the city and using a MYKI card will cost you less than $10 a day for unlimited travel on trains, trams and buses (trams are free in the central city zone). But it is also a great place to walk around exploring different neighbourhoods like Balaclava, where we came across this:
Balaclava is definitely becoming gentrified like neighbouring Ripponlea and Elwood. But Carnegie is still packed with affordable ethnic eateries including the excellent Paradai Thai. It also has great coffee all over the shop and the bagels at Huff Bagelry make a cheap, but filling breakfast.
On this visit to Melbourne I was accompanied by the boyf who loves his food and wine. This meant that we did visit a lot of fancy restaurants and wine bars. But we also went to some other cheaper places that I would go to if I was on my own. Like Don Don in the city which is a great place to get freshly prepared Japanese food for less than $10. This tofu curry was about seven dollars.
And of course there are lots of places you can enjoy for free. We went to both NGV galleries and the gallery in the State library. Libraries are often the best places to visit in cities and Melbourne is no exception. The Shrine of Remembrance is an incredible building to visit if you like 20th century history mixed with architecture that reminds you of a scene from Indiana Jones. The adjacent Botanic Gardens is always worth a wander.
Melbourne's beaches shouldn't be overlooked. Take a tram down St Kilda Road and get off at Elsternwick. Walk west, through the suburb of Elwood, stopping for coffee at one of the many great cafes and then keep on walking until you reach the bay. In the summer, the swimming at Elwood beach is the best.
If you have a bike, you can also cycle the whole of the seafront from there up into the central city. Look out for the scale model of the solar system along the path. Or if you want to go the other way (and it is summer), you can stop at the Brighton Sea Baths - basically a fence around the sea. A great place to people watch. Even if it is too cold to swim, there is a good restaurant with views over the water.