Real estate services to home buyers and sellers in zip code 77008 in Central Northwest Houston. Â Zip code 77008 is located near Greater Heights and Shady Acres. Search real estate listings and view homes for sale. Browse homes for sale in 77008, a zip code in Houston, Texas. For more info about any of these 77008 real estate listings, click the "Request More Information" button located on the detail page of each property.Â