Miami 24-hour food!
Here's a good starting point for a list of restaurants open 24hrs ->
Of these, places where I think you're likely to find edible food (though your ability to distinguish at certain hours may be impaired) would be ->
David's Cafe (off Lincoln Road) - decent Cuban
Sergio's (Coral Way and 32nd) - also decent Cuban, 24 hrs weekends only, I believe.
Not listed at that website ->
News Cafe (SoBe) is predictable if not exceptional.
Lester's Diner in FTL (on State Road 84 way east toward the port) is a classic old-school diner.
Can anyone vouch for the food at Yambo? I've heard of this 24-hr Nicaraguan place around Flagler and 17th but never been. Supposed to be completely wacky decorations to boot.