Houses And Apartments For Rent In Sunbury Ohio . Find your next apartment in sunbury oh on zillow. The average home rent in this town is $2,098. Charming rentals in Sunbury, OH Sunbury Pointe from cortland.com Apartment rent in sunbury has increased by 12.3% in the past year. Sunbury, oh apartments for rent sunbury is a terrific choice for your new apartment. The average apartment rent in sunbury costs renters $1,890.