I looked up the ASA
list of observatories for you (links where available) - no idea of opening hours etc but here you go, get those fingers walking through the phone book - or the online Telstra white pages
The Adelaide
Observatory
University of Adelaide
Observatory
Adelaide
Planetarium - University of South Australia
Private Observatories
DO3-12 Mr Justin Tilbrook, Private Observatory (Penwortham, SA)
DO3-13 The Stockport
Observatory (Astronomical Society of South Australia, near Adelaide)
DO3-24 Douglas Scrub Observatory (Astronomical Society of South Australia, near Adelaide)
DO3-34 The Heights School
Observatory (Adelaide SA)