BALCONES HEIGHTS, TEXAS. Balcones Heights is near the junction of Interstate highways 10 and 410, six miles north of downtown San Antonio in north central Bexar County. It was developed in the late 1940s and had a population of 950 in 1960 and 2,504 in 1970. The community was incorporated in the 1970s, and in 1990 it had 3,022 residents.