If you happen to cross the Yarra and head down to the South East, you may chance upon a scene that would suit somewhere in Europe.
This place is Greektown in Melbourne and has the requisite plateia (πλατεία or town square) where people come to stroll down and watch other people while enjoying a greek coffee and cake. There are only two or three main coffee shops to choose from but they are usually packed especially on a sunny Saturday afternoon. You can eat inside but it's all about the patio experience.
Be warned though, you'll experience a genuine Greek experience so don't complain about the table service, the next table is smoking or people are talking loudly. It's all the more authentic!
As an aside, the signed photo of Yiannis Plutarxos above the counter and pop music playing in the background was also a nice touch, although the music was drowned out by the customer's conversations.
I was once a foolish and misguided GAG (Greek against Greeks) and soon learnt the errors of my ways. Unfortunately, now I'm more of a YAY (a yuppie against yuppies) but that's another issue. In all honesty this place is great and you won't find a better place to enjoy an authentic Frappe in Melbourne outside Greece (other than a Greek home). There's also lot's of tasty sweets on offer, but we opted for more savoury offerings on this occasion. Note: The loukoumathes looked really good- a great incentive to return soon!