I just spent four days in Sydney, mostly babysitting and without a car. Thanks to Ry Beaver, I learned that there is a very active Facebook group called Australian Mammal Watching, posted an RFI there and got not just some good advice, but an invitation to a trip! Chris Charles and Murray Lord (thanks, guys!) took me spotlighting to Colo Gorge NW of Sydney. In a few hours we saw 3 spp. of mammals: two swamp wallabies and a common brushtail possum in the part of the gorge that’s outside Wollemi National Park, plus one species inside the park that was new to me: a Gould’s long-eared bat which we actually spotted at a night roost from a moving car (there are many small cave-like niches in roadside rocks and you can use your flashlight to quickly look inside without stopping the car). There were also some cool herps and three southern boobooks.
In Sydney I got a common ringtail possum and a few grey-headed flying foxes at University of Sydney campus (note that the colony at Royal Botanic Garden has been evicted), plus a totally unexpected barking owl at Clovelly Beach.
For people with more time, here is a page about mammals of Sydney with a few locations listed.