Furnished Apartments For Rent In Memphis Tn Under 600 . In memphis, tn, where the average rent is $626 per month, there are 23 units available for less than $600. 2743 ketchum road memphis, tn. Rent Cheap Apartments in Tennessee from 445 RENTCafé from www.rentcafe.com Compare prices, choose amenities, view photos and find your ideal rental with apartmentfinder. Considering that you are trying to spend as little as possible, looking. Sellers of these homes have accepted a buyer's offer;