General disclaimer about the area in winter- while not many places shut down for months over the winter like they used to, it's still common for the small businesses to shut down at some point for 2-4 weeks between now and late February so the do-everything owners can take a vacation, and winter hours are frequently shorter than summer hours. So it's a good idea to call ahead and make sure a place is going to be open before heading out.
I'm not a breakfast person, but I've heard good reports on Harbor Docks and Another Broken Egg (though Another Broken Egg sometimes gets criticized for being too expensive). There are also the obligatory eleventy zillion Waffle Houses in the region.
I like the Red Bar in Grayton Beach for lunch- food's always good and it's a great place to people watch. On Sundays, they'll have a local country or blues band playing for brunch. For good Thai food, I like Jasimine Thai next to Chan's Wine world in the Destin Publix shopping center. (If you want Asian takeout food, the Thai food is generally far, far better than the Chinese food in these parts).
Fabrice's in Watercolor Beach has some yummy French food in a very casual setting, and they've got a dangerous takeout pastry case. I've heard good things about the new Taste of Oz-
A Taste of OZ some slightly different offerings than what you usually get around here and the pumpkin soup sounds good during cooler weather.
Our favorite gumbo is at Kenny D's in Miramar Beach- they've got a nice dark roux to it. (A lot of other gumbos in these parts aren't roux-based)
Pizza- Ciao Bella has outposts at the outlet mall, and at the foot of the Destin bridge. Also good salads and sandwiches there, though I find their pasta overrated. Also near the Destin Bridge is McGuire's, which is generally reliable for casual steaks and seafood, though you need to be in the right mood to handle the Irish theme park environment.
Good grocery stores- Publix and Fresh Market. Fresh Market's got a pretty big deli & bakery area and a whole slew of prepared foods that pull together nicely for a picnic or quick dnner in.
Tourist traps that cruise by on a good view, serve lousy food, and the locals generally avoid- The Crab Trap, Fisherman's Wharf, The Back Porch, Pompano Joe's. (Though if you must, the crab dip at Crab Trap and the tuna melt at Pompano Joe's are probably your best options)