My mother and I will be 'stopping over' in SF for a couple of nights and would greatly appreciate advice on hotel's etc. We, unfortunately, will be using A$ so I think budget and/or moderate (as long as it's clean and secure)will have to suffice (although any suggestions are welcome).

Someone will ask or make a snide comment so I'll just nip that:
Australian dollars=A$.

The cheapest way to see SF is to stay away from the city itself and ride the subway in to visit then ride back.
There are some budget hotels in SF, but 'budget' means under $100 USD/night, and they'll be very basic.

I will suggest the Cornell Hotel. Nothing fancy, near Union Square (city centre), clean, family run (from France), superb French restaurant underneath, used to be (still?) very reasonable. http://www.cornellhotel.com

Try the King George on Mason St, a nice hotel for $65 a night.

Jane, a lot of people are getting great SF hotel rates through Priceline. For example, the Park Hyatt for $50 USD/night. But before you attempt to bid, go to www.biddingfortravel.com for a tutorial on how to use PL. The helpful board moderators will even help you construct your bid. It'll be well worth your time.

Came across a site hotelres.com a San Francisco booking service. Great search features. Had the best rates I located and with standard cancellation policies. I booked into the Monticello Inn for late Sept. for $77/night + tax.