Not sure how far from the airport it is but maybe Michaels Genuine. I’ve never eaten at the one in Miami but enjoyed the food at their branch in the Cayman Islands
You can go the their restaurant on Calle Ocho (or Versailles nearby) for Cubano. Michael’s is solid as is Michy’s. And since you have seven hours, go to Joe’s (it will take that long). The Eater 38 is pretty reliable as well The 38 Essential Miami Restaurants, January 2014 - Eater Miami
Versailles for Roast Pork & Maduros , banana chips, black beans & rice, Cafe con leche.
Come dressed as Castro & they will have a "special treat " for you !
Why not just go down to Calle Ocho and walk down the street until you see a fun window cafe serving cheap authentic Cuban fare. Go for lunch, order a media noche and a cafe con lechon y flan for under $10. Now that is authentic.
Some fun, swanky places on Lincoln Road in South Beach.
I second the vote for Michy’s. Expensive but creative, eclectic, amazing, with a nice wine list. Best restaurant in Miami IMHO.
Without a doubt go to Garcia’s on the Miami River. Seafood straight off the docks. Eat on picnic tables, drink freezing beer, while enjoying massive stone crab claws, fresh lobster and a great array of fresh fish, like Cobia, triple tail, Mahi, black grouper, wahoo, swordfish, etc. Drive up in your boat!