Well the
Australian Sister Cities Association - www.asca.asn.au - Home page should be able to help you or put you in touch with the office in your area. I had a look on Wikipedia and Brisbane's sister city in Japan is Kobe. If you contacted the City Council I'm sure they'll be able to put you through to the right people. If you're not in Brisbane just google the name of your city/town and "sister cities".
I got help from the Belmont Sister City Association (Belmont is a suburb of Perth though it's called a 'city') and also by asking friends of friends until I found someone who knew people in Japan.
Hostels can also be pretty cheap. All of the ones I'm staying in are less than 3000yen per night (about $33). I think it's good to have a mix of both. You kinda have to be on your best behaviour all the time with a host family. :P