At the time of the 2010 census , the population of Alamo Heights was 7,031 .
Alamo Heights is an incorporated city that is surrounded by the city of San Antonio in Bexar County in the U.S. state of Texas .
At the time of the 2010 census , the population of city   was 7,031 .
Alamo Heights is an incorporated city that is surrounded by the city of San Antonio in Bexar County in the U.S. state of Texas .