Hi Vaughn,
I am in the Melbourne suburbs as well, and I have found that targets like Omega Centauri can vary significantly from night to night, getting reactions from "wow that's amazing" to "no, that's ****, I am going inside".
Try the Jewel Box, Kappa Crucis Cluster, NGC 4755, which is an open cluster in the constellation Crux. Also try M6, M7, and NGC 6231 in Scorpio. These are easy to find open clusters and will look nice in all scopes.
It took me about 6 months to learn how to actually observe what is in the eyepiece. A bar-stool so you can be comfortable and let the object drift across the eyepiece a few times and catch that moment when the atmosphere settles and seeing is excellent. Averted vision is also a useful thing to read up about and practice for the fainter objects.
Epsilon Lyra is a nice "double-double" star, but you need a good northern horizon.
Good luck.
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