Budd, IllinoisBudd is an unincorporated community in section 2 of Sunbury Township, Livingston County, Illinois, United States. Budd is southeast of Streator and west of Dwight, Illinois. Budd has ZIP code 61313.HistoryBudd is situated on the Norfolk Southern Railroad,, nearly midway between the cities of Streator and Dwight. In 1909, William Cahill was in charge of the town's grain elevator and John Hughes ran a general store. There was also a post office which is no longer open.