It's weird but we actually enjoy watching some of the storms in Florida because the cloud formations are just spectacular and more frequent to what we get here at home (SE Wiscosnin).
This is the biggest excitement in a couple years - took this last Sunday night out our front door (here in Wisconsin):
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Some of the storms themselves are shows unto themselves in Florida. The nice thing is it rarely goes for long periods and if you catch a supercell during a sunset - you have some great photo ops!
The accuweater app will show you real time rain - how many minutes until it comes to your exact location and until it ends. I'd use that and head for indoor attractions/shows/meals when you see rain heading your way. As long as you don't mind running your GPS on the phone it's amazingly accurate. Just bring a couple power stick/banks.