Cheap Apartments For Rent In Jamestown Ny 14701 . Cheap apartments for rent in jamestown on yp.com. Jamestown features 729 low income apartments with rental assistance where households typically pay no more than 30% of their income towards rent. 11 Cook Ave, Jamestown, NY MultiFamily Home 19 Photos Trulia from www.trulia.com Refine your search by using the filter at the top of the page to view 1, 2 or 3+ bedroom apartments for rent in 14701 jamestown, ny as well as cheap apartments, pet friendly apartments, apartments with utilities included and more. Explore rentals by neighborhoods, schools, local guides and more on trulia! Additionally, there are 114 other low income apartments that don't provide direct rental.