One of my very favorite spots in Miami, The River Oyster Bar is an upscale but understated gem of a local restaurant serving very high quality seafood and shellfish in an urbane, refined setting.
Prices are reasonable given the very high quality here, and the place has an urban, sophisticated feel to it. (The ambience sits somewhere between that of a Manhattan bistro and Venice Beach's Abbot Kinney area.)
Particularly on weekends, the bar can get quite crowded (with both drinkers and barside diners), and the tables fill up quickly, so a reservation is essential.
Standouts for me typically include Northwest oysters, perhaps the best bucatini with lobster fra diavolo in town, and consistently excellent fish dishes.
Very conveniently located in Brickell, too. One of Miami's very best, in my view.
Recent update: I believe the River Oyster Bar is soon to be affected or even closed by the ongoing construction for a major new commercial and residential development across the street in Miami's Brickell district. Call ahead before you go.