Apartments For Rent Houston Tx 77084 . Explore rentals by neighborhoods, schools, local guides and more on trulia! We found exactly 118 apartments for rent in the 77084 zip code of houston metro, tx. Stoneleigh Apartments Rentals Houston, TX from www.apartments.com See all available apartments for rent at 17811 glenmorris dr in houston, tx. This property is 38 years old, it was built in 1984, and has 296 units. Broadstone park west (2) 2219 greenhouse rd, houston, tx 77084.