I'm quite fond of Lake Mountain but it gets better farther away you go from Melbourne. Any closer to Melbourne leaves me wanting, but L.M. is a good compromise at little over 1 hour from eastern suburbs. Mt Baw Baw is better but/because it's farther. Both around 1400m above sea level. I like observing from mountain tops because it gets you above the crud in the atmosphere and the worst of the seeing. But the best skies I've seen so far were near Seaspray just before 90 mile beach. Not exactly very close to Melbourne, but you get what you pay for so to speak.
But Arthur's seat and elsewhere on the Peninsula is good for how acessable it is. And there's no pollution source to the south.
For those in the western suburbs places like Snake Valley past Ballarat where we just had a star camp, thanks to Ken ballratdragons and Co, are good options.