One of my favourite places is the Dandenongs National Park – the park is bursting with wildflowers as I'm writing this. You can expect to see some flowers there from August to December. There are some great walking trails, including the extremely popular 1,000 Steps, plus a myriad of lesser known trails. See here and here for a map and route descriptions.
Another area well worth visiting is the Grampians National Park – I've just come back from a glorious wildflower weekend there. The Grampians are about 250 km west of Melbourne with a wide range of overnight hikes and day walks. There's a map here. And trail descriptions here.
I'd recommend the Wonderland Walk, a 9km day walk near Halls Gap (I found out about it from a small booklet I bought from the Halls Gap tourist office for the princely sum of $3.50). The wildflowers were just everywhere on that trail! (So many colours, so little camera battery).
Another place worth considering is Bunyip State Park, east of Melbourne. I love heading there for a little wildness and wildflower time. There are routes and a map here.
It's worth checking weather and road conditions on the Parks Victoria website before you go to most national parks though (in case of floods, fire or other good reasons to stay away). There were floods in the Grampians just before my trip and I was lucky the roads had re-opened. You can easily check conditions before you go here.
And if you prefer your wildflowers in a less wild setting, it's hard to beat the Cranbourne Botanic Gardens. I've had several Spring trips there and never tire of it. They even have a café if you need a rest from all those flowers!
If you have a favourite wildflower hike near Melbourne, please let us know by leaving a comment below. We look forward to hearing your suggestions.