There are Facebook groups for just about every subject imaginable. Not surprisingly, there are many country and city specific ones dedicated to business advertising. It's definitely worth joining several of these and being active on them. As well as being good places to advertise your page, services and products, you can also find lots of relevant, local Facebook pages on them that you can engage with as your page.
Many of them are for businesses anywhere in Australia. Given Sydney's large population, many of their members will be from the city, so your ads will seen by lots of locals.
Below is a list of some of the best ones I've found recently.
AUSTRALIA'S BUSINESS ADVERTISEMENT FOR SMALL BUSINESS ONLY NO RULESLocal Business AustraliaAdvertise in AustraliaAdvertising Australia GroupBusiness Advertising Australia Small Business Classifieds AustraliaAustralian Small Business Advertising - VIC NSW SA WA TAS NT QLDAustralian Business GroupFree Business Advertising Australia WideAustralian Business AdvertisementsBusiness Network AustraliaAustralia ONLY Business Advertising!Australia Business Group
And here are some that are specifically for Sydneysiders:
Sydney Local Business Advertising PageSydney, Australia; FREE AdsAdvertise Your Business in Sydney - no rulesI Am a Business Owner in SydneyStart-up Job - SydneySydney skill share - Tagg