I don't know since I took the bus tour when I visited. I recommend Google areas for parking.
In front there is a place. Just look up Towers address for your GPS and it'll take you right to front door. Have fun! And Groupon has discounted tickets
I walked, get tickets on Groupon.
I parked in front of government building since it's Sunday you won't get towed
Also the bus tour has to let's that includes a boat ride and a bus tour of all of San Antonio and free pick up for the whole day
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