First, Florida has a lot of coastline, and within 1 to 2 miles of the beach is very affordable (but will obviously vary from place to place.) We bought a house a little over a mile from the beach at a very low price in the Fort Lauderdale area.
Next, a lot of people move here for 2 to 3 years based on their vacations and then move back after they go through a solid time period of the heat, humidity, and weather/hurricanes. I don't want to jinx it, but we in So Fla have been lucky with the hurricanes for the last 5 years or more, so you forget how bad it is sometimes when there is a direct hit or even a near miss. I lost a car once in a tropical storm, not even a hurricane. I agree with you, though, I'd rather deal with that than snow and ice - especially the way they seem to have gotten more vicious up there in the last few years.
They say the gulf coast has nicer beaches. I lived in Tampa for less than a year and just thought it was dirty and too spotty. I really didn't like it. Even if you find a nice neighborhood, a lot of "downtown" is just not cute.
If you guys like Disney, I'd go closer to Disney. Or again, the Melbourne area is not too far and very nice. And I think closer areas like Winter Park and so forth are nicer than Orlando or Tampa. JMO!