I do light trail hiking with my Pyrenees at Hardburger Park, Walker Ranch Park, McAllister Park and Eisenhower Park several times a week because they are all located in north central San Antonio are are easily accessable. Outside of town, Lost Maples and Bastrop that were mentioned are two of my favorites but require a little travel time. Also requiring a little travel time but well worth it are Enchanted Rock State Park, Garner State Park, Hill Country State Natural Area, and South Llano River State Park.
Closer to town are Government Canyon State Natural area and Guadalupe River State Park which are just outside of town and great places to hike. Government Canyon has 40 miles of trails including more challenging terrain and Guadalupe River State Park has about 5 miles of trails as well as a 4 mile stretch of the river to play in.
Check out the Texas Parks & Wildlife website for more information and ideas.
