I lived there for two years and played quite a bit of golf there...
If you are looking for a reasonably priced morning round and then a nicer and more expensive afternoon round I would suggest:
1) Olmos Basin course in the AM....this is a municipal course located along US 281. It is a decent muni and well maintained. The price is downright cheap....if you are willing to drive a bit between your rounds, Cedar Creek is the best of the munis and is located on hilly terrain in the NW part of the city. Once again, all of the municipal courses are very very reasonably priced.
http://www.sanantonio.gov/sapar/cour...=1024&ver=true
2) In the afternoon drive less than a mile away and play The Quarry - which is rated one of the top 100 public courses in the Republic of Texas...I loved this course and its back nine is really interesting. It is inside an abandoned limestone rock quarry. Once you descend into the quarry the sheer walls of it loom above you as you play the back side.
This is an upscale course with an upscale price but worth the memory....
http://www.quarrygolf.com/