San Antonio...

Which base?  They hold some triathlons and road races at Ft Sam so I assume running on base is good. And it's not too far from Brackenridge Park, and drive a bit further and you'll be at McAllister Park (be prepared to get lost on the trails!).  There's a park right next to Camp Bullis with some trail running areas.  Not so sure about Randolph or Lackland. 

Brian

fort Sam Houston has a 4 or 5 mile loop and and outdoor track if your looking for speed work out. Randolph air force base has an indoor track. Close to Randolph (5-10 minutes drive) in Schertz and cibolo there are some good (wide) roads to run on around Cibolo valley road and some country roads with little traffic.