Hi Dan,
Hot tip for you from a former Royal Melbourne Hospital-ite and Monash Medical Centre-er...
Most hospitals have an online, staff only trading post type thing on the staff intranet. At my last job at RMH, there were ALWAYS places up for rent near the hospital that were listed only at the hospital... ie, in some cases taking over leases from hospital staff who were going overseas, or the landlord was a hospital staffer also (thus, had access to the listings), and preferred to lease to other hospital staff. From memory, there were some quite nice places.
Hope this helps, especially if you already have your email access, or a friend who can help you out
Mish
