I live close to the Kay Bailey Convention Center and there is parking available all around the convention Center available to the public. Parking anywhere downtown isn't free anywhere. If you don't want to worry about finding a parking place close by, take the red or blue line to the Dart Convention Center. It's literally a 5 minute walk across the street from the Convention Center.
You can park on the convention center parking garage. There's a fee for that. It was $10 when I went there but it might depend on the event.
There are several parking lots near by.
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