I have lived in Austin for 28 years and without a doubt Zilker Park is my favorite thing about this city. Some weeks you can find concerts such as Blues on the Green, ACL, Reggae Fest, etc (the list goes on). On weekends it's a great place to go for a hike or ride a bicycle. You can play sand beach volleyball or take your dog out to the open greens and throw a ball around.
Be forewarned, the weekends can get very busy, so it is helpful to get there early if you want to find parking. By about 1:00 P.M. you can expect issues with traffic and parking.
You cannot visit the ATX without going to Zilker Park and just hanging out. It is the Austin experience.
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