It's not actually illegal in many places in the city. For instance, it's perfectly legal (as far as i know) to drink booze in flagstaff gardens. The Melbourne City Council
has a series of maps on their website (ctrl + F "Liquor").
If you're not totally drunk or disorderly, a lot of people will ignore it, especially if you don't look very suss (i.e. unfortunately homeless or violent looking). It also helps if its in a generally accepted place like a hot day at the beach or a few people sitting on the grass at a park with a picnic basket or something. Context is everything.
Even then, it's not like they'll haul you off to jail, at most you'll get a fine or they'll tell you to tip it out. If you do want to avoid suspicions, if it is a liquor or spirit, i suggest you mix it into a slurpee or something like that then drink the slurpee. If its a beer, you might like to go to McDonalds, get a large cola cup, drink the cola and fill the cup with beer or wine. I've only ever done the slurpee thing, even then we divide it among like 5 people. That said, i'd rather go to a bar than wander aimlessly and i reckon you should consider your view on bars again, take a few friends.
As always though, drink responsibly. Keep in mind alcohol does have a fair few
harms and dangers associated with it. All things in moderation hey?