Finding things for small children is tough. Especially in a a city populated by young hipsters, it seems the city more caters to that scene as opposed to toddlers and the like.
Kiddie Acres has been in Austin since 1979. That's right 31 years of catering to kids, so you know they have it right.
I went when I was a kid. My Grandparents would pick us up from time to time, and we would spend the day out there.
There are a multitude of rides, with a miniature golf course, all reasonably priced, so if your kid starts screaming, you can leave, and come back, and never lose a dime. I find that to be one of the major selling points as my Daughter is going through a phase.
For $20 she got to ride all the rides once and left with a balloon. Who doesn't like balloons.
She's 3 and about thirty pounds. There wasn't one thing there she couldn't do. She seemed to enjoy the pony ride more than anyhting, and an interesting side note to that. If you went when you where a kid, there's a good chance your kid will be riding the same pony. My Brother went with us and sure enough if it wasn't the pony he had ridden 17 years earlier.
If you are in the Austin Area, and you are looking for amusements for the young ones, nothing beats Kiddie Acres.
Amusement Park & Miniature Golf, Children's Birthday Parties | Austin, TX