A possibility between St. Augustine and Miami is Jonathan Dickinson State Park in Hobe Sound. You'll like Curry Hammock ( at least we do). If you want to get closer to KW, BluewaterKey at mile marker 14.5 is very nice. Closer in , on Stock Island is Boyd's and ElMar... you can easily bicycle to Duval from either one.
Red Coconut and San Carlos are both good places at Ft. Myers Beach. Another place right on the beach is Turtle Beach CG in Sarasota. Another place we like is Venice Resort ( CG) on the Myakka river