We have a place in Destin and try and get down there 4-5 times per year. Needless to say, we love it down there.
Our hands down favorite restaurant is The Red Bar http://theredbar.com, which is in Grayton Beach, about a 20 minute drive. They only have 4-5 items on the menu each night, but I promise you the food is excellent, and it's one of the more reasonably priced places around.
I'd also reccomend breakfast at Another Broken Egg. They have a few locations (one in Destin, one on 30A towards Grayton Beach, and one in the lobby of the Sandestin Hilton.
Mcguires Pub, which someone else mentioned, is very good, but a bit pricey.
Finally, we really like AJ's for their blackened grouper. AJ's is down by the fishing docks. After dinner you can step outside and walk around the marina and over to a new little shopping area nearby.
If you have any other Destin questions, feel free to PM me. Enjoy your trip...