The Parkes Observatory does open days for one weekend each year. The next one is in early October:
http://www.parkes.atnf.csiro.au/news...opendays/2011/. You get to wander around the whole place including inside the observatory building that forms the support for the dish (unfortunately there is no playing cricket on the dish itself
). I highly recommend it (and the annual open day at the optical observatory at Siding Springs too)