Geneseo is the name of a town and a village in Livingston County in western New York, USA. The town's population is approximately 9,600, of which about 7,600 live in the village. The English name 'Geneseo' is an anglicization of the Iroquois name for the earlier Iroquois town there, Gen-nis-he-yo. Geneseo apartments for rent comparison page shows most up to date rent information on Geneseo apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.