Red Bud isle - On lady bird lake by the longhorn dam. I would recommend going early in the morning during the week to avoid the crowd. This spot, as you may know, is a dog park and can get pretty busy on the weekends. Follow the trail all the way to the end and fish off the point.
Lady Bird Lake - Park by the Holiday inn off 35 & Riverside. If you head west down the bank there are a few spots with good access to the water.
If you are feeling adventurous, take an ultra light down to the greenbelt and fish the creek. It is loaded with bass. I was down at spyglass a couple weeks ago and the water was in great shape. Crystal clear and flowing nicely