Miami is hot and humid. I would recommend visiting during winters (Nov-Feb). You can fly directly or use it as a stop over for visiting the Caribbean or doing a Carribbean cruise
Unlike Chicago or Boston, Miami does not have good public transport, so, I would recommend renting a car.
Day 1
Start the day with a visit to Seaquarium for a Dolphin show.
Follow this with a visit to Everglades National Park, do watch the show here, and get a chance to hold an alligator or a snake in your hand.
In the evening, make a trip to the Ocean beach.
Day 2
Drive to Key West, it is a 3 hour scenic drive through several small islet (keys) connected via a land bridge. Unlike Miami, Key West is walk-friendly.
See the southernmost point of the United States.
And checkout the street shows in Mallory Square.
Day 3
Key West has a unique concept of adventure cruises that consist of day cruises consisting of Parasailing, Jet skiing, snorkeling, and ocean kayaking. I have never seen them elsewhere and I would highly recommend doing them while you are in Key West.