The closest airports in the area are
# Choctaw Nolf airport (NFJ) located about 9 miles northwest of Navarre in Milton, Florida
# Hurlburt Field (HRT) located approximately 10 miles east of Navarre in Mary Esther, Florida
# Eglin AF Aux Near 3 Duke airport (EGI) located roughly 26 miles northeast of Navarre in Valparaiso, Florida
# Bob Sikes airport (CEW) located around 33 miles northeast of Navarre in Valparaiso, Florida and finally
# Mobile Downtown airport (BFM) located about 73 miles west of Navarre in Mobile, Alabama.
The Hurlburt Field and Eglin Air Field airports are probably not accessible to civilian airplanes, as they are both Air Force Bases. I doubt if there are scheduled flights to most of these airports.
More realistic airports include these three (with their codes)
* Destin/Fort Walton Beach/Okaloosa County Airport (*VPS)
Main airport for the Destin/Fort Walton Beach area.
Situated on Eglin Air Force Base in Valparaiso Florida, 850-651-7160.
* Pensacola Regional Airport (*PNS)
60 miles west of Destin 850-435-1746.
* Panama City - Bay County International Airport (*PFN)
60 miles east of Destin 850-763-6751.
Access to the Navarre beaches on the barrier island was by toll bridge. But after three hurricanes (Dennis and Ivan in 2004 and Katrina in 2005, many out of area contractors were needed to do repair work. For rebuilding operations, the contractors need easy access to the island, so the bridge is not currently a toll bridge.