I stayed at Sun n' Fun when visiting friends in Sarasota a few years ago. If you can't find something fun to do there, you simply can't be entertained. They even had a carpenter shop with all kinds of power equipment if you want to be a wood butcher. But Sun N' Fun wasn't cheap.
The panhandle gets chilly in the winter months. I was stationed on an aircraft carrier in Pensacola for two years, compliments of the Navy. I've been back since then, and saw people walking along the beach, but they were wearing light jackets. Nobody in the water.
But the panhandle is also home to the National Naval Aviation Museum. A must see for both adults and children, as many items are "hands on". And if you're lucky, the Blue Angels will be practicing as its their home base. There are bleachers behind the building.
When I was in the Navy, I don't think planes had been invented yet. :)