Some have already been mentioned, but here are others:

River Place Nature Trail

Wild Basin Wilderness Preserve

Mount Bonnell (not much of a hike)

Blunn Creek Preserve

Turkey Creek Trail

McKinney Falls State Park

Enchanted Rock

Colorado Bend State Park

Milton Reimers Ranch Park

Lost Maples State Natural Area

Garner State Park

Balcones Canyonlands National Wildlife Refuge

Guadalupe River State Park

Pedernales Falls State Park

Texas Wanderer