For the ultimate in flexibility, there is nothing to beat camping; either with a tent or with an RV (recreational vehicle).
There are hundreds of campsites (campgrounds) across Florida including many within the various State Parks.
These will give you access to hiking, biking, canoeing, horse riding and fishing amongst beautiful surroundings.
If you do hire an RV, make sure you understand how everything works and remember that you will typically get around 8-10 mpg so though you will not have to unpack every evening, you will need to fill up more often!
When checking the price of campgrounds, note that unlike hotels and motels, they typically charge based on two people; you will often have to pay extra if there are more than two adults (children usually go free).
Facilities will vary between campgrounds but most will offer 30/50 amp service, water, electricity and sewerage, paved parking, picnic areas and some even offer cable TV and wireless internet access.