Though not a cycling club, Bike North BUG at
http://www.bikenorth.org.au/ which have regular rides ranging from easy to hard. see there rides page and calendar.
Some of the muggacino riders are also members of Bike North or also ride with Bike North.
Bike North objectives is to run regular social rides and advocacy for and on behalf of cyclists. They plan and work with councils on the North Shore including Mosman Council.
You do not need to be a member to go on their rides
Michael G.