Windsor, Balaclava Close to South Yarra with little less rent than expensive rentals in South Yarra.
There's some nice South Eastern suburbs that might be suitable for you.
Glen Iris is about 40 minutes from South Yarra via train, 2 minutes from the freeway and has access to Bus/Trams.
Bentleigh East & Moorabbin both are good for public transport as well as schools, parks, shops, cafes and friendly locals :)
If there is no restriction on commute time or distance, the Mornington Peninsula is a great area to set up base. You can enjoy the beaches and holiday lifestyle.