The city center has loads of hotels, but occupancy levels are high. Even so, Friday through Sunday nights, when the business travelers go home, can be quiet, so ask about lower rates on weekends. You may strike a deal on a weeknight if business is slow. Many hotels throw breakfast or some other feature into weekend packages. Most hotels have rooms for travelers with disabilities. If you can't find a hotel that suits you, there are several B&Bs to choose from in and near the city; check www.babs.com.au/02_wa/perth.htm for details.
In Fremantle -- There's something of a perpetual holiday atmosphere in this picturesque port city. Public transport for the 19km (12-mile) journey to Perth's city center is good, especially the train. So you can happily explore all of Perth from here -- and many top attractions are in Freo as well. There are good restaurants and a happening nightlife, too.