Yes I agree with Alex about Royal and Heathcote NPs e.g. these might suit but check them out first:
Some parts of the Coast Track such as Bundeena to Marley
Curra Moors Circuit
Lady Carrington Drive
Forest Island
Palona Cave
Lake Toolooma/Mt Westmacott circuit
Pipeline Trail
Also if you are prepared to travel to the Blue Mountains there are several firetrails and other walks less than 2 hours drive from most of Sydney that have zero or not a lot stairs. A few that come to mind that in my recollection may be suitable:
Charles Darwin Walk
Mount Hay Wall and Butterbox Point/Hay Monolith
Braeside Walk
Popes Glen Walk
Burramoko Ridge Trail to Balzer Head overlooking Hanging Rock
Mount Banks firetrail and summit - These have been closed recently due to bushfire damage so check the current status first
Blue Gum Swamp Creek circuit (easy) - Can extend it to Grose Head South lookout, no stairs but some very steep hill walking
Lockley Pylon is mostly easy though there are one or two short rocky descents/ascents and reasonable number of steps to access the pylon summit itself
The cliff top tracks around Katoomba and Leura
Radiata Plateau
Grose Road FT to Faulconbridge Point Lookout
Another place that might suit is Barren Grounds Nature Reserve near Robertson in the Southern Highlands
Nearby also is Minnamurra Rainforest. No stairs from memory but a couple of very steep hills (short ones though)
A bit more research I'm sure will reveal enough to keep you busy for some time.
Also try the advanced search on wildwalks as you can restrict it to the types of walks that may suit you. Look at the terrain summary for each walk for a description of what to expect:
http://www.wildwalks.com/bushwalking/general/search-for-a-bushwalking-track.html