For San Antonio proper, and a few of the other towns in Bexar county, the best two districts are Northside, and Northeast. Northeast is a more expensive area, in general, but the Northside school district is considered just as good. The state of Texas has their ratings, for whatever they might be worth, on line.
http://www.tea.state.tx.us/perfreport/account/index.html
In general anything outside loop 410 and north of the I-10/US-90 line is fine, outside, or near loop 1604 is even better. Even the school districts to the far southeast aren't bad.
If you have any specific area, and thus specific schools, in mind, FReep mail me. My wife is chair of a teacher education program at a small college in Texas, so she has her own sources. She/we don't live in San Antonio, but we have in the past, and hope to retire there, and may move back before we retire. We will probably have custody of our great nieces now almost 8 and 6 1/2, so we are looking at school districts down there as well. (Our daughters have a JD and MA respectively and the MA is working on her PhD.
There's some good information on San Antonio linked at
http://www.swri.org/6swsa/live/live.htmNorthside ISD
Northeast ISD
Texas School District Locator
St. Mary's San Antonio links, including School Districts