Bingara is a small town on the Gwydir River in Murchison County in the New England region of New South Wales, Australia. Bingara is curreā¦Bingara is a small town on the Gwydir River in Murchison County in the New England region of New South Wales, Australia. Bingara is currently the administrative centre for the Gwydir Shire that was created in 2003. The Gwydir River is part of the Murray-Darling catchment area.