Cheap Apartments For Rent Staunton Va . The average apartment rent in this town will cost you $1,086. We provide a cost calculator, pricing tools, and more so you’ll know exactly what it will cost to live in the city you love. 3612 Staunton Ave Apartments For Rent in Charleston, WV from www.forrent.com When you use apartments.com, finding a cheap apartment in staunton is a breeze. The average home rent in this town is $1,439. Browse 1 cheap apartments for rent in staunton county, va, priced from $1,485.