If you only wanted to have a casual fish, you could give the rock wall a try. When you come out from the ramp into the Brisbane River, just keep going to the other side. You will soon see the wall. Careful not to hit it if you are there on high tide as the section of the wall once it leaves the shore gets covered.
Or, you could try the end of the wharf at the mouth of the river. Head out, and then when you are at the end, turn right. Lots of boats fish along the exposed wall.
No reason not to go to Mud. There is nothing to hit. It is 10m all the way across from the mouth to the island. I have never had much luck on the west side (usually the protected side), but a lot of the plastics guys do ok drifting along the 10m dropoff approximately between the west cardinals. Lots of structure in closer to the island that you can sound out, but I have never done any good at Mud during the daylight hours. I usually fish the late afternoon into early evening, and on the eastern side.