Cheap Apartments For Rent In Zanesville Ohio . What does cheap mean for apartment rentals in zanesville, oh? You might be interested in studio apartments , 1 bedroom apartments , 2 bedroom apartments or 3 bedroom apartments , or browse all rentcafe apartments for rent in zanesville, oh. Sandhurst Apartments Affordable Community, 3139 Sandhurst Drive from www.publichousing.com See all 2 apartments under $600 in zanesville, oh currently available for rent. 1259 muirwood dr, zanesville, oh 43701. You can watch out for bargains using the price drop option, and you can also sort and filter listings according.