The Austin area is full of them. We have a gajillion city, county & state parks to choose from and most of them are really great. I haven't been to all of them, only a few. But, I have seen or heard about a bunch more than I have been to and I can't wait to go visit them soon.
Some of my favorites are: Zilker, Emma Long, Mt. Bonnell, Town Lake and Circle C. You can search this handy site on Austin360 to find the perfect park for your outing: http://www.austin360.com/news/content/recreation/guides/parks/search.html.
Enjoy our great weather this time of the year. Do what I did the other day -- go fly a kid with some little kids. It's amazing how much joy they get from holding the string handle on a dragon kite with a ten foot tail as it soars only a couple of hundred feet above their heads. And, I could just lay there in the grass, relax and listen as they talked about their dragon.
AC