On TV the ABC, Channel 7, Channel 9 and Channel 10 all have state-specific broadcasts and newsrooms while SBS runs a single national program. Because the capital cities in Australia make up such a large proportion of the population you will rarely get "local news" on TV if you live in a regional town or area.
Most regional and local papers are owned by either News Corp or Australia Community Media (which was formerly owned by Fairfax before they were acquired by Nine) though, so even these local news outlets rely on the big players.
If you live in Melbourne's north I recommend trying to get a hold of "The Local Paper", which is an independent paper that focuses on things like what the local council gets up to. It's a pretty different experience to reading one of the big mastheads.
Similar for radio. ABC has local radio programs that are bulked with national programs. Triple J supports up and coming artists and alternative tastes, is ABC funded, and has local productions including in country towns around the country.
The real issue here is Facebook and Google scalping the news content and reselling it as their own.
The bigger issue is that Murdoch media undermines everything and needs to be broken up.
I would say local newspapers and radio are the majority of local news sources though.