Cheap Apartments For Rent In Boyle Heights . As an average rent for a studio apartment in this neighborhood is $1,762, and has a range from $1,000 to $3,133. Apartments for rent in boyle heights, ca. 41 Apartments for Rent in Boyle Heights, CA Westside Rentals from www.westsiderentals.com As an average rent for a studio apartment in this neighborhood is $1,762, and has a range from $1,000 to $3,133. Find your next cheap, affordable apartment in boyle heights los angeles on zillow. 5 beds • 6 bath