If you want to do it like a local, here are a few hole in the wall spots that I think you'll enjoy.
Clive's - This Miami mainstay has been around since as long as I can remember (40 years+). This great Jamaican spot got priced out of Wynwood a few years ago and is now located a few miles north in Little Haiti. Their jerk chicken is absolute fire and some of the best I've ever had. Can't go wrong with the ox tail or goat neither. Platters come with 2 sides (I love their rice & peas and macaroni salad) and go for about $10-$16, more or less depending on the meat you order.
Conch Town USA - This spot is another mainstay here in the city of Miami, located across the street from Miami Jackson HS. Used to love going there for lunch when I was attending the J. Don't go there as much as when I was younger because they're usually closed by 7pm but they have not lost their touch. Whether it's a conch salad, fritters or fried chicken, the food is worth making that run for lunch. Only downer is that it's small and unless you can get a seat at the counter, you'll probably have to take it to go.
Plaza Seafood - Located in the heart of Allapattah, just west of Wynwood. This spot hasn't been around as long as the first two restaurants I mentioned, but has been in business 20+ years at least. And since the NY Times ran a story on them a few months ago, this place seems more full than usual. Open for lunch, but you better get there early. You order at the counter and find a seat at one of the outdoor tables. I don't think I've ever tried anything here that I didn't enjoy. Whether it's their soups, empanadas, conch salads, or fried fish, you can't go wrong with anything off their menu. Did I mention they have a market in the rear of the building where you can pick up fresh fish, stone crabs, shrimp and just about any other assortment of seafood to go and cook at home?
Garcia's Seafood - If you want to pay a little bit more and get some table service then you may want to try Garcia's. Same family owns La Camaronera, but Garcia's has been around a lot longer. Traditional Cuban plates with seafood (or marisco as they say in Spanish). They also have a fish market on site.