Actually, the towers that are downtown are about 600 feet tall. If you go up in the Tower of the Americas, you're just about level with their tops.
Go to the FCC's website below, you can search for tv and radio towers with the advanced search form. The site lists their heights and locations. The heights are in meters, so you have to convert them.
http://wireless2.fcc.gov/UlsApp/AsrS...tionSearch.jsp
Going by that, the tallest tv or radio tower inside San Antonio's city limits is 968.83 feet tall. There probably are taller tv and radio towers, but they might be outside of San Antonio's city limits.