Stafford Run Apartments Share: Apartments Stafford Run Apartments 550 Stafford Run Rd. Stafford, TX 77477 (281) 499-9534 (281) 499-6151 (fax) About Map About One & two bedroom apartments. Call today! We'd love to tell you all about our great community. What's Nearby? Distance: 5 10 15 20 25 50 mi.