There's a father's only playgroup that meets at the Kirribilli Neighbourhood Centre at 16 Fitzroy St. Time, Tues 10-12. Starting Feb 7th. 0-2.5years olds Dads! Fathers! Male owners of newly born babies, infants, toddlers, children!
It's run by Kindergarten Union and the North Shore Health Service(?). One of the nice things is that they have a staff member trained in child psychology who has been a great help. I've been able to pepper her with questions and get great answers. The playgroup kids and equipment is good fun. There's about 9 or so dad's that go to that one. See link at http://dad.s-pla.net/
There's a father's play 'n chat in Sydney run by Marrickville Council that meets 1st and 3rd Saturday at Petersham Park. It's also associated with the Magic Yellow Bus so there's great toys available too. I heard there may be changes to the schedule of that group so best to call the council for more details.
Just passing on info.