Hope this isn't too late, but I lived in Tallahassee for a couple years during college. This was 20 years ago, but I used to fish a place called Wakulla Beach. It's still open to fishing, it looks like. It's at the end of Wakulla Beach Road, maybe a 45 minutes south of Tallahassee. That's where I'd go.
Around peak tide you can fish along the marsh grass for reds and sea trout - the former on anything crabby looking (or one of my Softy Spoon flies), and the latter on a chartreuse Deceiver or similar.
Otherwise you can walk a few minutes west of the beach to Goose Creek - a tidal creek/marsh - and fish the oyster bars. It's easier if the tide is not too high, but it's almost always good for fish.
Fwiw, I made my peace with God on Goose Creek. I was fishing, waist deep in the middle of the creek, minding my own business, when suddenly two gigantic black sea monsters came surging up the creek directly towards me. I was too startled to piss myself. I took a deep breath and thought, "Okay, if this is how I go, so be it." About fifty yards away from me, the beasts started swimming in circles in the middle of the creek, and large mullet start popping out of the swirl. They were pilot whales, herding mullet - one of the most amazing things I've seen in the wild. I was grateful to witness it, grateful to have lived through it, and then half an hour later I was kinda pissed they had completely blown out the creek.
There are also some good largemouth bass lakes in the area, which might be a plan B. There's not any one I prefer over the others - they all have fish.
-Miles