As previously mentioned, try Lane Cove River Tourist Park
www.lcrtp.com.au
We stayed there in our tent last March and certainly recommend it, but best to book in advance during busy times and weekends.
Train station is only a short walk from the park, and a few stops and you are right into the middle of the city centre.
Although the park is only a few KMs from the CBD, it feels rural - except for being on the flight path for the airport.
Would definitely stay there again.
Paul