Think about making your new house in Arizona in one of the areas that offers the lowest cost of living. Sierra Vista. One-bedroom average rent price: $663. Yuma. One-bedroom average rent price: $759. Tucson. One-bedroom average rent price: $835. Casa Grande. Courtyard Apartments was the source for this information from Rent.com. Mesa. Goodyear. Glendale. Avondale.