One organisation that comes to mind is ARAFMI Hunter. They are an organisation who aim to help carers of people with a mental illness. On their website their is a page for local support groups - which I hope you find helpful!
And of course you can use these forums as a type of support group - obviously it's not face to face - but it's here 24/7 if you ever want to drop by 
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Help us push aside the stigma and discrimination surrounding complex mental health and change the way people talk about, and care for, mental illness.
SANE acknowledges the Aboriginal and Torres Strait Islander peoples as traditional custodians of the land on which it operates. We pay respect to Elders past, present and emerging, and value the rich history, unbroken culture and ongoing connection of Aboriginal and Torres Strait Islander people to country.
SANE values diversity. We are committed to providing a safe, culturally appropriate, and inclusive service for all people, regardless of their ethnicity, faith, disability, sexuality, or gender identity.
Help us push aside the stigma and discrimination surrounding complex mental health and change the way people talk about, and care for, mental illness.
SANE acknowledges the Aboriginal and Torres Strait Islander peoples as traditional custodians of the land on which it operates. We pay respect to Elders past, present and emerging, and value the rich history, unbroken culture and ongoing connection of Aboriginal and Torres Strait Islander people to country.
SANE values diversity. We are committed to providing a safe, culturally appropriate, and inclusive service for all people, regardless of their ethnicity, faith, disability, sexuality, or gender identity.
