Drummoyne SC is an option but! as it is very shallow at low tides, be careful! On Tuesday night there was an Endevour 26 tied up there at the lowes low tide.
The other two options are the Woolwich Marina which has a public jetty but it is a bit of a lee shore in strong southerly, south easterly winds.
The second one is on the Birchgrove side at the end of King street next to the swimming pool.
It is the best spot around by far. The jetty is the same type as at King George park (Callan park).