Apartments For Rent Near Cortez Co . List and sell your home on! Rentals.com was built with parents in mind. 1009 Catalpa St, Cortez, CO 81321 Trulia from www.trulia.com See all 3 apartments in cortez, co currently available for rent. 2 beds • 1 bath. Within cortez we have 7 rental houses spread across multiple school districts.