"Low" season here in Florida is always August and September, because they will either be the hottest, or have storms (or sometimes hurricanes, but don't let this scare you away!) Schools here generally go back in mid-August, so from mid-August to mid-September are decent times to go (if you can stomach the weather) because no one wants to schedule a family vacation when the kids have only been back in school for two weeks.
Spring break is basically all of March (because some schools it's early in the month, some it's middle, some it's end) so not a great time to go.