Starting with Newcastle, naturally, there are 8 or so Ukestras (ukulele orchestras) and two choirs run by the monumentally committed, energetic and fun people at The Sum of the Parts (music).
Below are links to other groups in Australia that provide people with places to meet, maybe learn a bit and play ukulele music together Let me know about your group and I'll add a link or contact details to the list.
Bad Boys of Uke - Cairns (Qld)
Blue MUGS - Blue Mountains Ukulele Club (NSW)
B.U.M.S. - Brisbane Ukulele Musicians Society (Qld)
CUB - Canberra Ukulele Band (FB page)
CHUG - Cairns Holloways Ukulele Group (Qld)
Central Coast Ukulele Club (NSW)
GRUB - Goulburn Regional Ukulele Band (NSW)
Kempsey Ukulele Club - FB page
MUK - Melbourne Ukulele Kollective (Victoria)
Nambucca/Bellingen/Urunga (NSW) - the leader's FB page
NUTS Northside Ukuleles - Sydney's Northern Beaches (NSW)
Swingaleles - Wollongong (NSW) Club Fraternity, Fairy Meadow, Weds 7 - 9.30pm
TUGS - Tuggeranong Ukulele Gang in Canberra (ACT)
Uke Central - Cooloola Cove (Qld) (formerly Woy Woy, NSW)
URoC - Ukulele Republic of Canberra (ACT)
for groups in the USA and Canada, this list at Ukulele Hunt is very comprehensive
Send me a link if you'd like your group included.