I can give you a spot to avoid, especially for light sleepers: Navarre Beach. It's the home of the Air Force's weapons testing department at Eglin AFB - we were treated to 2 nights of "nighttime helicopter warfare" that sounded like it was happening about 2 blocks away. It went on from about 1 AM to 6 AM, and the explosions/machine-gun fire was scary even when you know it's only practice. I can't even imagine how upsetting it would be for a Vet suffering PTSD. The locals don't even seem to notice it, so I guess you learn to tune it out? They said it happens a couple times each month, and we were lucky enough to be there to experience it.
A nice little park that's oceanfront, in the middle of nowhere, is HoHum RV Park in Carabelle.