3 Things to Know in the Housing Market Today! 12802 Highland Hills Drive, Cypress, TX 77429 This single-family home is located at 12802 Highland Hills Dr, Cypress, TX. 12802 Highland Hills Dr is in Cypress, TX and in ZIP code 77429. This property has 4 bedrooms, 2 bathrooms and approximately 2,649 sqft of floor space. This property has a lot size of 1.01 acres and was built in 1983.