The short answer: avoid summer. From June through September the heat is punishing — mid-90s with humidity that makes it feel like 100°F — and hurricane season runs right alongside it. Theme parks hit peak crowds at the same time because schools are out, which compounds the misery.
Fall (October–November) is genuinely the best window. Crowds thin out, prices drop, the weather turns comfortable, and you can still swim. Winter brings the "snowbirds" — northern retirees who colonise the coasts — but the weather is mild and there's plenty of activity. January and February can occasionally dip into the 30s in the north of the state.
Spring is a mixed bag. March and April are lovely, but May kicks off the rainy season and things get muggy fast. If you're visiting for spring break, expect company: Daytona, Key West, and Panama City Beach draw enormous college crowds through March.