There's a small strip of bushland in Earlwood's Girrahween Park. It takes about 20-30 minutes to walk along but there are times where it actually feels like you are in the bush. There are also nice little areas to sit and have a picnic, including caves or by Wolli Creek.
You can enter from Hartill-Law Avenue or Sutton Avenue and the walk will take you through to Turella Reserve. For railway access, get off a Bardwell Park and turn left up Hartill-Law Avenue. You can access Turrella station at the end of the walk.