The Most Valuable Square Inch in Houston Could Be Your Dream Home. Afton Oaks is an older neighborhood that is centrally located just inside Loop 610. It is a small upscale neighborhood of about 525 homes that are a mostly 1950s ranch style homes and a few new construction homes. It is nestled in one of the most exclusive areas of Houston neighboring River Oaks. Afton Oaks is just minutes from downtown, the Galleria, and Rice Village. The people who live here are a mix of wor