You can bring water bottles but no outside food and no coolers. There's a picnic area inside the park at the back of the parking lot, before you go into the zoo. You could bring cooler with food and have picnic there. Check the website rules, http://www.jacksonvillezoo.org/content.aspx?pageID=15994&CNM=Park Rules
Don't know about a cooler but I would bring some kinda bag that keeps things cold? For your water and other drinks?
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