Shuckers, in the Island Beach resort, is on your way back from the beach! We ate there last winter, was jammed on a Sunday but good food and ambiance. https://www.islandbeachresort.com/dining/

We go to Blind Creek a couple of times each winter, was just there a week ago, in fact. Hope your weather is good, it's a crapshoot in February sometimes. We're at Cypress Cove all winter, cypresscoveresort.com. Maybe you consider staying there instead of the Hyatt? It's a half hour from the airport at that time of day.

Be sure you mention to the hotel people that Blind Creek is the reason that you are visiting. It's legal now and making good progress toward becoming "official":
https://cbs12.com/news/local/st-lucie-county-could-be-a-step-closer-to-having-official-nude-beach