Apartments For Rent In Azuza California . The average voucher holder contributes $500 towards rent in azusa. In addition to the rent cost, you need to also account for costs of basic utilities consisting of. 43 Apartments for Rent in Azusa, CA Westside Rentals from www.westsiderentals.com The median azusa, ca rent is $2,869 which is above the national median rent of $1,469. Try rentals.com to compare amenities, photos, & prices to find apartments that match your needs. Apartment finder has you covered!