Yes, you can find bargain basement accommodation in Sydney. No, you don't have to sleep on the beach or in some backpacker's lodge to get it. There are some decent, clean, cheap Sydney hotels in the suburbs of the city that will suit the flattest of pockets.
The best tip any traveller to anywhere can get is to look for reviews on the internet. If you find an advert online, or even a website, for a certain hotel, you should immediately look for reviews from others who have stayed at the hotel.
The best hotels allow reviews on their own websites, but there are many independent places on the internet where people leave reviews. Just type in a term such as cheap hotels in Sydney reviews and you will be taken to the relevant place.
Reviewers are generally kind about the places they have stayed. They are also very informative about the standard of service, the facilities and the general ambiance of the place. If the hotel attracts enthusiastic bikers or noisy revellers, these reviews will warn you in advance.
Similarly, the reviewers are always ready to give a bouquet rather than a brickbat. If they receive extreme consideration from a member of staff, or if the hotel has a lovely swimming pool or garden, they will say so. The internet has changed the way we regard travel bookings. Make the most of it.

Travel to Westbourne: Find many reviews on Travel and accommodation.