Greene County Oh Apartments For Rent . 1651 stewart blvd, fairborn, oh 45324. Greene county oh apartments for rent. Beaumont Greene Senior Living Apartments, 13710 Della Dr., Athens, OH from www.rentcafe.com View our greene county real estate offices and let us help you find the perfect rental or apartment. In addition to the rent cost, you need to also account for costs of basic utilities consisting of water, garbage, electric and natural gas. Browse photos, get pricing and find the most affordable housing.