Illawarra native birds are a diverse and interesting lot, with 440 species recorded in Terrill Nordstrom's 2020 book, A Guide to Birdlife of the Illawarra Region of NSW.
With our diverse ecology and coastal areas, the region is home to everything from tiny Gerygones and Weebills (qualifying for the 'Small Brown Bird' designation) to majestic Pelicans, massive Powerful Owls and White-bellied Sea-eagles. And the urban realm is home to many of these species, which depend on parks and gardens, and even patches of weeds, as well as remnant and recovering native vegetation.
Pretty well any area can contribute to habitat for native birds, as long as you plan carefully and provide what they need.

Take, for example, the Brown Gerygone (Gerygone mouki), a small native bird that feeds on insects low down in shrubs and trees. This little critter is recorded living in rainforest, wet sclerophyll forest (i.e. moist Blackbutt or Bluegum-Bangalay hybrid forests), along forested riparian corridors and even in overgrown urban parks and gardens.
Supporting this bird is as simple as giving it more of what it needs and keeping threats to a minimum. So let your garden, or a corner of a local park, grow wild and shrubby; grow local native species suitable to your area; avoid using insecticides that will kill this species' food; and keep cats and dogs indoors so they don't disturb or kill the birds or destroy their eggs.
And the Brown Gerygone is just one of many small birds that call the region home. Spotted and Striated Pardalotes also eat insects but tend to forage high in the outer branches of trees. White-browed Scrubwrens hop around fearlessly in urban parks and gardens, feeding on insects, other small invertebrates and grass seeds. All benefit from more native plantings in gardens and other urban settings.
One particular tip is to stick to truly local natives, and avoid the showy grevillea cultivars that attract aggressive larger birds such as the Noisy Miner. While this species is native to Australia, they benefit from typical urban plantings, with showy nectar-rich flowers and lots of 'edge areas' around remnant forest patches. It can take a while to acclimatise to the smaller flowers of many local plants, they have their beauty and interest if you take the time to observe and appreciate them.

For many larger birds, of course, large areas of habitat such as forest, shoreline or wetland are essential. No individual gardens can provide these. But working together, groups of neighbours can contribute to the preservation or even the restoration of habitat, including large hollow-bearing eucalypts suitable for species from gliders to possums to owls.
Avoid cutting down eucalypts if you possibly can, rather prune them for safety and to maintain habitat. And do your best to convince neighbours to hold onto theirs too.

Each species has its own preferences and habits of course. You can manage for many of these. For more information and tips, check out local zoologist Garry Daly's informative article on attracting native birds.
There are also many books available on gardening for birds, though none with a truly Illawarra focus. And Birdlife Australia has an online course on habitat gardening for birds, which again gives general information, on its website.