I have an aunt that lives in Sarasota that I go down and visit. Ive been sun burnt on that beach many times.
I've successfully use beach sand for bronze casting although it wasn't as perfect as pure fine silica sand would be. There is a process for sorting abrasive grit called elutriation which involves in one case a flow of water from below which depending on the flow rate causes the lower density and finer particles to overflow the container. Think of a bucket of sand with a garden hose pushed down to the bottom and flowing water through the sand and overflowing the rim. Set up properly, all the lighter organic matter and soluble stuff like salt should be removable.
Siesta is nice, but lovers key further South is quieter. I know of a couple other spots, but refuse to tell anyone where they are at. Few places left in Florida where you can spend the day at the beach and not see a soul all day.