We recently asked a local mum from the Ryde/North Sydney area what were some places they like to go for family outings, and this is what she suggested: 

North Ryde RSL that has an indoor Tribal Zone – up to 3 yr old are free then its $6 per child for 2 hrs.

North Sydney Playgroup is another favourite

Lane Cove Library offer’s on a Thursday at 11am an hr off song’s, crafts and story time and other session’s on different day’s depending on ages all free

Berry Island is a good park for barbeque’s and has a great park for all ages (two different section’s).