Best is sneakers or something like work boots, lot of tree roots along some paths
COMFORTABLE shoes like sneakers or the like. There are plenty of trails to hike. Some lead to the Manatee River and the longest trail heads over to Manatee Boulevard. If you enjoy botanicals stop over to the Palma Sola Botanical Gardens which is right next door; worth your time. Both venues are free of charge.
Tevas or similar as they are comfortable for walking but perfectly okay to wear if you walk in the water!
As mentioned by everyone else, wear comfortable shoes and I would also suggest sneakers. Keep in mind you may get your feet wet somewhere along any of the trails. And you also have the option of jumping into the bay for a cool off swim. There are no steep climbs here, you are in Florida at sea level; the steepest climb you will encounter will be the Calusa Indian mounds. You might consider renting kayaks for a cruise through the mangroves and the lower bay area shoreline. It's all natural with plenty of wildlife to view.
You would do best with shoes in which you would be comfortable walking through a natural terrain. There are some natural paths here and there and also, a bit of climbing (although not steep or difficult).
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