I like the "fish-of-the-day" at this place:
http://www.frenchquartergrilleaustin.com/
They give you a choice of several different fish (my favorite is the redfish) and can choose how its cooked (grilled, fried, or blackened. Their gumbo is amazing too. Take a little of the garlic butter that comes with the bread and melt it in the gumbo. Gives it a silky texture and accents the flavor. Its also a small place for an intimate atmosphere.