I know that I always seem to mention car hire as the best way to get around in Florida, and Im right too. But for a relaxing break, and if your mobility is good, then Siesta Key is an ideal place to just relax, and walk around.
I know, who would have thought I would ever suggest walking anywhere, but if you get yourself some digs close to the North, you can take lovely, very long walks along a very long beach. Enjoy the bars and diners, and enjoy the nightlife and people of this truly beautiful place.
A rental car is the best bet. I am not sure of the public transportation in Siesta Key/Sarasota area. I do know there are cabs. Yet the fee would not be cost effective.
Sarasota/Brandenton Airport does have commercial flights arriving and departing.