Siesta Key, Beach Access 12
This is the access point I use. The lot holds fifteen to twenty cars and people come and go constantly, so there's usually something open, especially on a weekday. Come a few minutes early anyway so you're not hunting for a space while the light is going.
The sand is the reason to put up with the parking. It's close to pure quartz, which is why it stays cool enough to walk on barefoot at the end of a hot day.