I've got to dissent here a bit on Dewey Destin's. They've been rather hit or miss over the winter. Not horrible, but at times rather ordinary, and they tend to over sauce their grilled offerings at times.
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In Destin proper, Harbor Docks does well on the fresh seafood front. They also supply fish for a number of other area restaurants, including La Paz (some interesting Mexican style fish offerings there)
If you're looking for really off the beaten path, take FL 20 (the road on the north side of Choctaw Bay between the Mid Bay Bridge and the 331 Bridge) to Nick's on Basin Bayou. Cement block and 70s furniture charm, and the sides are rather ordinary. But they really know their fish, and the view over the bay is beautiful.
Go to Louisiana Lagniappe in Sandpiper Cove for dinner. I believe it has re-opened. It was closing in October for renovations. Their fish dishes are amazing!
I can't believe Louisiana Lagniappe is owned by the same restaurant group as Back Porch. If this is true, they are like oil and water. Louisiana Lagniappe has been in business for some 30 or so years. I have never had a bad meal there, in fact, always walk away awestruck. Not over the top fancy with grape leaves, etc., just delicious Louisiana seafood! I was born and raised in New Orleans for 30 years (yes, it took 30 years to raise me). Moved to Atlanta 21 years ago with my husband because of his career. Of course, we both go home a couple of times and year. Mostly to eat, but of course, to visit friends and family also!!!!!!! I actually had the fried shrimp at Dewey Destin. It was very good. I don't think I'd eat fish there.