In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described Balby like this:
BALBY-WITH-HEXTHORPE, a township-chapelry in Doncaster parish, W. R. Yorkshire; on the river Don 2 miles SW of Doncaster r. station. It has a post office under Doncaster. Acres, 1,567. Real property, £4,844 Pop., 1,058. Houses, 241. Tanning, brickmaking, and sand-digging are largely carried on. The living is a vicarage in the diocese of York. Value, £150. Patron, the Rev. R. J. Banks. The church was built in 1847. There are a Wesleyan chapel of 1868, a P. Methodist chapel, and a national school. The Quakers, under George Fox held their first meetings here.
GB Historical GIS / University of Portsmouth, History of Balby, in Doncaster and West Riding | Map and description, A Vision of Britain through Time.
Date accessed: 25th April 2017
Click here for more detailed advice on finding places within A Vision of Britain through Time , and maybe some references to other places called " Balby ".