Unclear what exactly you mean by "iconic".
If "local institution" is the intent, Joe's Stone Crab probably best fits the bill but stone crabs are out of season. (AG, Joe's website says they are reopened for dinner as of May 20) ->
I don't know if they serve frozen claws in the off-season but I'd rather go in season anyway.
If by "iconic" you mean reflective of local flavors, I think that Michael's Genuine Food & Drink and to a somewhat lesser extent Michy's would be at the top of the list, as well as Ortanique, OLA, Chef Allen. The latter 2 I have not been to in some time.
I give a strong recommendation for Ortanique on the Mile. It is truly a Miami Icon. For 16 years Cindy Hutson's cuisine continues to win accolades and represents best the Floribbean movement of the early 90's. She is undoubtedly the heir to Norman Van Aken and the Mango Gang chef's who put south Florida on the culinary map. Her restaurant is the quintessential Miami dining experience.