Mr VFR, I would try Aldinga Aerodrome for aircraft hire. I did recently, and had a great experience there. I had never flown in Adelaide, and found these guys to be very professional and excellent in presentation! I think they call themselves Adelaide Biplanes or something like that.
Also the best flying school presentation I've ever seen! I would gladly leave guests there whilst I would fly, and know they would enjoy it, and the food, and viewing area. .... And right next to the McLaren Vale wineries - thats all I was there for
Anyway, look up on net for them ... Great bunch. Cheers KP