Cheap Apartments For Rent In Elizabeth Nj . The average apartment rent in this city costs $2,344. 908 lafeyette | 908 lafayette st, elizabeth, nj. Grandway Apartments Elizabeth NJ Apartments for Rent from bestrentnj.com The average apartment rent in this city costs $2,344. As of may 2022, the average apartment rent in elizabeth, nj is $1,065 for a studio, $2,160 for one bedroom, $2,020 for two bedrooms, and $1,757 for three bedrooms. 1 to 2 bedroom affordable housing apartments from $950 up to $1069.