Step 1--Find a golf course, any golf course, that you can either walk to or park near.
Step 2--fish the back nine at dawn.
Step 3--fish the front nine at dusk.
Honestly, any freshwater in Florida is going to house big largemouth bass.
If you want to fish the salt, there will be fish in the surf that time of year, but I have no fly-fishing experience with that. I grew up bait-fishing and spin-fishing Gulf Shores, AL.
If I were in Destin in May, I would try crab flies--sand fleas (see link below) are a common live bait in the surf on the panhandle (the gulf coast version is almost always more of a cream color than in the wikipedia illustration, but they are occasionally grey). Pompano would be my primary target, but Redfish are possible. Speckled Trout may also be around--they like baitfish, but are opportunistic feeders. All three taste real good. If Bluefish are around you'll know it because they'll show up in marauding schools and the birds will be diving like crazy. Some kind of baitfish imitation fly like a clouser or deceiver would be my first try (with some sparkle--yellow, red, and white colors work) and a toothy critter leader; combined with a cast that can reach the schools should result in tons of fun. Some people don't like bluefish for eating, but I've found that (if you cut off the tail when you catch 'em and fry 'em up that evening) gulf coast blues taste pretty good. They don't get as big as on the East coast, but they're a good fighter. Ladyfish are fun, and jump like crazy, but their flesh is no good for eating.
Saltwater catfish are trash, and their dorsal fin is sharp and toxic. Be careful if you're wearing sandals.
Sand Flea wikipedia