All I could find is this map: https://www.microburbs.com.au/heat-map/cars-per-household#151.21574744788342:-33.84319955763839:13 but I'm not sure where the data is sourced from. It does show lower car ownership in more central areas of Sydney.

And this, but it only splits by "greater metropolitan" type areas, which would obviously include outer suburbs: https://profile.id.com.au/australia/car-ownership?WebID=260

It does show there is slightly lower motor vehicle ownership in cities broadly, and I'd anecdotally expect that to be lower within inner suburbs.

And for Brisbane: https://www.brisbanetimes.com.au/national/queensland/where-in-brisbane-do-people-own-the-most-cars-search-for-your-suburb-20230712-p5dnou.html

indicates higher car ownership as you go further from the CBD, although it only compares 3 or more cars vs less than 3.

EDIT: Oh and this quote from the Brisbane Times article:

The top five suburbs with no cars were in the inner-city with more public transport and walking options – Brisbane City (40.4 per cent of homes had no vehicles), Bowen Hills (29.2 per cent), Fortitude Valley (28.7 per cent), Spring Hill (23.8 per cent) and South Brisbane (21.9 per cent).