I've always wanting to visit Florida but not the tourist attractions. I want to see raw beauty 
It is surrounded by lots of nice quiet places actually, and because it's bordered by the Gulf of Mexico and the Atlantic ocean, there is a lot of coastline to enjoy.
I can't wait to go one day, I absolutely loves beaches and oceans! 
Although it is the 8th most densely populated of the US, there are still places where there is unspoiled beauty and not all the tourist trappings, like St. George Island.
That's probably where I'd be going then. Do you know any other interesting facts about Florida?
Keep in mind much of the state is at or near sea level, so if you are there during hurricane season and one comes, it is best to evacuate if they tell you to.  
That is very scary, I'm terrified of floods in general. I would just go when it's not hurricane season. 
Probably pretty wise, just remember that the more southern Florida you visit, the more it's a tropical climate, so places like Key West would probably support outdoor vacations all year round.