O'steen's is a must, and has the best minorcan chowder. Go slightly off hrs, like between 2 and 5, for less crowds.
The Columbia in downtown does have excellent cuban food, love their 1905 salad. They actually have their own parking lot,located behind the restaurant on Spanish street.
Also downtown on St george street is the Spanish Bakery, only open until 2 or so, they have great cheap empanadas.
There's a place on St george street called cafe hidalgo, i believbe its spanish, and has a tapas and cocktail bar above it, but I've never been so can't vouch for it
And on Avilles street, which is on the other side of the square from the big tourist area, and a really lovely area to walk around, is La Harencia cafe, with some very good cuban food, and good breakfast too.
That's all i can think of for now. Our 2 big specialties are probably fried shrimp and minorcan chowder. If you want some key lime pie, go down to publix supermarket and get a whole one from their bakery, they are excellent