I was under the impression that LBL was trying to ban bank fishing because of the hooks that end up on the public walking trails. Could have been resolved.
There is an ordinance banning fishing on the new boardwalk, so basically anything east of the Shoal Creek confluence isn't allowed. How well that's enforced though is open to speculation.
If you can find permanent water in Austin, you will find fish there. I loved fishing Barton Creek and Bull Creek and found some great bass and carp there. When I was bored and had an hour to kill I would take my two weight fly rod to the pond behind Central Market on 45th and Lamar and catch Rio Grande Cichlids and Green Sunfish. If you can get up early enough to beat the dog walkers, Red Bud Isle has some great fishing when they are pulsing water through the dam. After work I would park on 9th and walk up and down Shoal Creek trail and find lots of sunfish and small bass.
The moral of the story is you don't have to go very far to find great fishing in Austin. Don't over think things, but remember that clear water + lots of water activity means spooky fish, so don't be afraid to size down both on lines and lures. All of my PB bass have come on size 6 and smaller flies.