near the Biltmore Hotel, Coral Gables
There really isn't much that is walking distance from the Biltmore since it is in a residential area. A short taxi ride away you can go to Downtown coral gables or Merrick Park. In Downtown gables there are many restaurants, however, none of them really specialize in fish. There's bonefish grill but that's not really local just a chain. La Cofradia usually has great fish dishes as does Francesco.
The Biltmore has a great brunch on Sundays and their restaurant Palme d'or is quite good.
Hopefully, someone will name a place that I can't think of right now.
Key West by the Gables 2238 Red Road went there a little while back. Nice place with comfy decor and clean inside of old grocery store. The food was good and prices were reasonable for portions. Try the crab croquette and fried shrimp. This place is not far from Biltmore at all.
There's great fresh fish at ArtFish on the Mile. I've eaten there twice and both times the food has been excellent, though very empty. I was initially terrified of eating in an empty seafood restaurant as I'm quite picky about seafood, but they maintain it very well. Great crabcakes too.