The national map with the boundaries for all local government areas is available at: https://www.nationalmap.gov.au/#share=s-aJS6sDWNcRYfERcqeod1fxAoeEP
Additional details about council maps and boundaries may also be available via the state-specific links provided below:
VIC
https://www.vec.vic.gov.au/ElectoralBoundaries/LocalCouncilMaps.html
NT
NSW
http://www.olg.nsw.gov.au/ or http://www.screen.nsw.gov.au/page/maps
QLD
https://results.ecq.qld.gov.au/local_area_maps/
SA
https://www.lga.sa.gov.au/sa-councils/councils-listing
TAS
https://www.lgat.tas.gov.au/__data/assets/pdf_file/0027/322983/Local_Govt_Area_A4_map.pdf