If you are looking for rentals in the Sun City area I found this website that might help. It looks like there are a number of rental properties and vacation rentals for Sun City. http://www.suncitiesarearentals.com/sun-city-rental-properties.htm
Here is a place for examples of rentals rentals. http://www.homes.com/rentals/sun-city-az/residential/p12/?orderby=price desc Local newspapers have rentals as low as $695.