According to this article from The Bradenton Herald via the Emergency Management Magazine website, folks in Southwest Florida, Central Florida and the Tampa Bay area will find the availability of emergency shelter during the next hurricane to be in short supply. Some of the shortages cited in the study that the article is based upon are staggering.
Looking at these predicted shelter shortages, I would say that if a destructive hurricane (category 3, 4, or 5) is coming your way and your home is in one, both, or all of these areas it might be best to evacuate as soon as possible and drive north until you’re out of the path. Otherwise, your chances of finding emergency shelter in your area look to be greatly reduced.