I'll give you a few places in different areas in and around Miami. If you want to head out to South Beach, my absolute favorite is Larios on the Beach. (This was the original location for the Estefans' restaurants, and the menu used to build Bongo's on.) It gets loud though! I also think all trips to South Beach should include the News Café. You can sit outside and people watch! Great atmosphere.
Heading over to Coconut Grove, I love Chart House, although that gets pricey (one of my favorite restaurants here in Jacksonville). Monty's is also a fun place to hang out, and is right on the bay. For a casual but good food place, Greenstreet Café rocks! Great sidewalk atmosphere. It's a bit hidden, but a simple Mapquest check will get you there.
If you want to head out to Key Biscayne (just a few minutes from downtown), Rusty Pelican is a good place to have a meal right on the bay/water.
Versailles over on Calle Ocho (8th Street) is excellent! But plan on a long wait!
Let me know if there is a specific area you would like to see, or if you wouldn't mind going even further out.