Power Without Glory by Frank Hardy . Based on real people and real events.
The Sentimental Bloke by C J Dennis
On the Beach by Nevil Shute
The Getting of Wisdom by Henry Handel Richardson.
Definitely second the Corinne Chapman series by Kerry Greenwood, so good!!!
Also, if you like mysteries with some humour, 'Brunswuck Street Blues' by Sally Bothroyd was really enjoyable. Highly recommend
A million votes for the Corinna books. Also Eaglehawk by that author’s not-husband. Resurrection Man by Sean Williams has Melb but not in an especially recognisable way.
The four months I spent in Melbourne last year were absolutely wonderful, so I was also looking for books set in Melbourne to bring home. The one novel that fit this category that I found was Almost a Mirror by Kirsten Krauth:
Murray Whelanseries by Shane Maloney - Murray is a political aide to a labour MP in state parliament who has to solve a murder before it (generally) brings down the government or he gets murdered. Also a series of films startting David Wenham (and directed by John Clarke)
Death in Brunswick by Boyd Oxlade - it's set in Brunswick and is a little weird to be honest and the main character is definetly not likable. Movie stars Sam Neill and John Clarke co stars
The Holiday Murders by Robert Gott - set in 1943, there's 4 books in the series (though by the end of the second book I was done with it). There hasn't been a movie about this one, presumably because John Clarke didn't read it