There are two possible airports, first Southwest Regional Airport (RSW) and Punta Gorda (PGD).
Southwest Regional Airport from the car rental center is 42 miles approximately a 1 hour drive, Punta Gorda airport is 35 miles and approximately 50 minute drive.
If you will not be needing a rental car, then Pine Island Taxi may be of help, here is their website Airport Transportation Pricing | Pine Island Taxi & Limo, Inc. | Pine Island, FL