It is comparatively cheap compared to SF, London, NYC and Sydney though...
Everything is relative. Personally I find it a very affordable place to live for a number of reasons:
1. I don't need a car (~$10kAUD+ a year) because transport is sufficient.
2. Queen Vic and South Melbourne markets are very accessible which make buying fresh ingredients for home cooking very affordable.
3. Entertainment is cheap, tons of cheap live music acts, art exhibitions, markets, etc.
4. Public transport is cheap (~$20/month, more if you don't live in CBD though)
5. AUD is declining against USD, by mid-2019 it's likely to be around 0.65 USD so if you make USD it's great.
6. Rent is relatively affordable. ~$1600AUD/month get you a 1 bed place in the CBD.
Those are just the money factors.
As I said, it's not "cheap" but it's "relatively affordable" meaning that you can buy an awesome life here with a bit more money than traditionally cheap places but achieve a better $/Quality of Life metric.
Melbourne would beg to differ; there were headlines when we lost the first place position a few months ago after quite a few years at the top.
Not proposing Melbourne as an alternative though, while it's a nice place to live it's far from cheap.