A.C.
I really like the children's pool at the East Austin YMCA. It's just off 183 at the intersection of 51st or 52nd. I plan to take my now 5-month-old there this summer. I wish they had pictures online, but here's their Web site: http://www.austinymca.org/locations/7
The kid's pool area has a sloped entrance to the water, so little ones should be able to sit in the water and splash around. For bigger kids, there are places to climb, shooting water, and other fun stuff. Hope this helps. Best of luck in your search!