Question: What town, which is about 30 km south of Gulgong, is the center of the Mid-Western Regional Council local government area in New South Wales, Australia?
Context: Gulgong is a 19th-century gold rush town in the Central Tablelands and the wider Central West regions of the Australian state of New South Wales.  The town is situated within the Mid-Western Regional Council local government area.  It is located about 300 km north west of Sydney, and about 30 km north of Mudgee along the Castlereagh Highway.  At the 2016 Census, Gulgong had a population of 2,521. The Mid-Western Regional Council is a local government area in the Central West region of New South Wales, Australia.  The area under administration is located adjacent to the Castlereagh Highway that passes through the middle of the area in an approximate southeast-northwest direction. Weabonga is a small village on Swamp Oak Creek, about 37 km south west of Walcha, 33 km south-southeast of Limbri, New South Wales, Australia.  It is in the ridges of the Great Dividing Range and is part of the Tamworth Regional Council local government area and Parry County. Jerangle is a locality in New South Wales, Australia.  The locality is in the Snowy Monaro Regional Council local government area, 366 km south of the state capital, Sydney and 112 km south east of the national capital, Canberra.  At the 2016 census , Jerangle had a population of 96. Shannons Flat is a locality in the Monaro region of New South Wales, Australia.  The town is in the Snowy Monaro Regional Council local government area, sandwiched between the southern border of the Namadgi National Park in the Australian Capital Territory and the Murrumbidgee River.  Shannons Flat also adjoins the NSW suburbs of Yaouk, Bolaro, Murrumbucca, Bredbo and Billilingra.  It is about 308 km south west of the state capital, Sydney, and 70 km from the Australian national capital of Canberra.  It is just over 40 km north west of the regional centre, Cooma. Rylstone is a small town in New South Wales, Australia, in the Central Tablelands region within the Mid-Western Regional Council local government area.  It is located on the Bylong Valley Way road route.  At the 2006 census , Rylstone had a population of 615 people. Ilford is a small town in New South Wales, Australia, in the Mid-Western Regional Council.  It is named after the small English town of Ilford (then in Essex, now in east London), where the founders of this town came from.  It is situated around 220 km north west of Sydney.  It is located on the Castlereagh Highway, which is locally referred to as "Sydney Road".  The Bathurst-Ilford Road (MR 54) (which comes from Bathurst and skirts past Sofala) joins the Castlereagh Highway on the northern outskirts of town and the Bylong Valley Way to the upper Hunter Region via Kandos, Rylstone and Bylong joins the Castlereagh Highway 2 km north of town. Hillgrove, is a Northern Tablelands (New South Wales) village with population of about 95.  The village is located approximately 30 km east of Armidale and is 5 kilometres south of the Waterfall Way.  Hillgrove is part of the Armidale Regional Council local government area and is in Sandon County.  This historic goldmining town is situated at elevation of 1,000 metres on a granite plateau above Bakers Creek and near the Oxley Wild Rivers National Park. Michelago is a locality in the Monaro region of New South Wales, Australia.  The locality is in the Snowy Monaro Regional Council local government area, 54 km south of Canberra on the Monaro Highway.  It was founded in the 1820s, on the main route from Sydney to the Snowy Mountains.  At the 2016 census , Michelago had a population of 562. Mudgee is a town in the Central West of New South Wales, Australia.  It is in the broad fertile Cudgegong River valley 261 km north-west of Sydney.  Mudgee is at the centre of the Mid-Western Regional Council local government area.  At the 2016 census , Mudgee had a population of 10,923 people.
Answer: Mudgee