The Alfred manages the busiest trauma centre and the largest hyperbaric unit in the southern hemisphere, and has the only adult burns unit in Victoria/Tasmania. Other areas of specialty are HIV/AIDS, heart/lung transplantation (including pediatric even though there isn't a pediatric unit, which worries me a bit but it's not my problem!) and adult cystic fibrosis.
It has a reputation among union officials as having a very anti-union nursing management, but this applies primarily to taking inductrial action, and all agreement conditions are met and sometimes exceeded.
Joanne's right that the Alfred's on the fringe of the city proper (ie CBD), but it's located in the inner suburbs, about fifteen minutes from Finders St station by tram and well supplied with public transport access (train, tram and bus lines nearby). Parking's a little less convenient but there is car parking on campus (at a price) for permanent staff.
Hope that helps - and congratulations on your decision to move to Australia's most livable city unless you want to buy a place to live (our less official title!)
http://en.wikipedia.org/wiki/The_Alfred_Hospital