Austin’s Zilker Park ranks fifth out of the ten best US city parks according the readers of USA Today.
A quote: “This 351-acre park within sight of downtown is arguably Austin’s most popular park. Highlights include miles of hike and bike trails, train rides on the Zilker Zephyr miniature train, a playscape for kids and a natural swimming pool (Barton Springs).”
There are plenty of events going on there as well. My favorite is the kite festival, the oldest kite festival in the US.