Here is a map where we have been taking our pugs to go swimming. Usually we meet up on the weekends and let the pugs swim around in the water.

This is a street map of the area:

Below is a more detailed map with landmarks:

I usually park on the street behind Chuy's restaurant and take the footpath down to the hike/bike trail, through the train tunnel to the other side.
Once I've crossed Barton Springs Road, I walk down the trail to Barton Creek past the canoe rentals.

A word on the parking in Zilker Park. On the weekends, there is a $2 entrance fee per car. Usually the lots near the creek are full, but you can try.
Walking distance from behind Chuy's to the creek is about .5 to .75 mile, but it's a nice trip and gives the pugs a chance to dry off before getting
back into the car.

I hope these maps help everyone find the place. :-)