Lots of car parks offer Earlybird rates..in before 9am and out by 6ish for somewhere between $11 - $16 per day or a discount for monthly parking. Would be cheaper to catch tain or bus though. Bus / train timetables link: http://www.adelaidemetro.com.au/
Yes, my wife paid $12 a day at the car park at Frome St, cheaper on Sundays. If it's a permanent job, you can get a permit for the hospital car park if you go on a waiting list - think it's about $34 per fortnight.