There are several great parks for hiking within hours of San Antonio. A few of my favorites are:
Lost Maples State Natural Area
Enchanted Rock State Natural Area
Colorado Bend State Park
Note that Colorado Bend has two types of camping--primitive and ultra-primitive. There are no water or electric hookups and access to the park is via a ten mile dirt road. This does, however, provide a nice atmosphere of quiet and seclusion. If you go during the week, you may very well have the entire park to yourself. A big plus is that Gorman Falls is open anytime now. It used to be only accessible on a once-a-week tour. They also have walking cave tours on selected weekends.
Lost Maples and Enchanted Rock can get very busy on weekends so advance reservations are highly recommended (especially when the bluebonnets start blooming).
Good luck!