I really doubt this is where you're thinking of because it'd be way out of the way, but there's the Regency Bridge. Its one of the last remaining suspension bridges in Texas. Its a one lane and spans the Colorado and is extremely high.
The bridge is just outside of Goldthwaite, TX but down some back road out in the middle of nowhere. Last time I was there you could still drive over it and you could hear the old wood planks moving beneath you.