Have a look at Jetts, they have one in the CBD already and are opening up another one pretty soon (on top of the 24/7 gas station on Pulteney street)
They seem to be a no-frills operation, 24/7 access but only limited staffing and seemingly cheap (they state 12$ a week on their homepage). Can't comment on well maintained the facilities are or what crowds show up, since I have never been to one.
You could try the gym at UniSA, City East campus. The other end of North Tce from the new RAH, near the old RAH.
It could suit your requirements, opens at 6am, has no frills and reasonable price. General public fee is $65 per month, $115 for 3months and cheaper if you pay for 6 or 12 months. You also can use the pool at Magill Campus, 15min drive east of the CBD
like the look of Jetts and UniSA, think I might have to go and have a look at those when I arrive, thanks guys.