Restaurants on Anna Maria Island that cook your catch.
Most of these places will cook you catch multiple ways (fried,blackened,grilled), and come with 2 sides for 10-15$.
I'm going to list them in no particular order. All have Live music.

Swordfish Grill in Cortez
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Mar Vista

Seafood shack
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Beach house

Tide tables in cortez
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Sandbar