If you can get to Lady Bird Lake (dammed colorado river where it runs through downtown) it has special bass regulations which makes it a very good fishery. Suuuuper clear water in most of it with trails and bank access along the majority of it. Kayak rentals are also pretty inexpensive if you wanted to do some yak fishing.
Also make sure to eat some P Terrys while you're there, best fast food burgers in existence! If you want to stuff your face go to Big Bite on the west border of UT, 888 for awesome Pho, Salt Lick BBQ is so worth the drive (to the original one in Driftwood not the one in Round Rock), Austin's Pizza, and for breakfast Juan in a Million downtown or Taco Shack.