Bank fishing in Austin is not the easiest thing to find that's forsure. Picking up a kayak would be a great investment down there. There are some giants in lady bird lake but it's almost impossible to fish without a kayak. You can also check out lake pflugerville just outside of Austin and you can bank fish that entire small lake. But have you ever checked out Austin fishing forum? You might find/get better info there, but regardless welcome to the forum!
A few weeks ago I bank fished at lake Georgetown. I fished at Overlook Park and Cedar Breaks park. I walked around a lot and fished. I caught fish up to 2.5 pounds on a Texas rigged zoom trick worm in watermelon red. The better fish came from overlook park.
You can also check out lake pflugerville just outside of Austin and you can bank fish that entire small lake.
I started out bank fishing Lake Pflugerville last year before getting my kayak. It is a little over three miles around the lake and there is a bike/jogging path along it along with four fishing piers and several small docks. I have been having luck fishing the weed edges for bass.