Key West
Southernmost city in the continental US is Key West. Key West is about 160 miles south from Miami and you will get there via US 1 route. That whole trip down should take you about 4 hours of driving, but usually it is little longer than that.
You would have a hard time to visit all the little Keys on the way down to Key West. There is 34 little islands connected together via bridges and accessible by car. Many of them are state parks or reservations. Last of them all is Key West. The Florida Keys are an archipelago of about 1700 islands in the southeast United States, and they would be accessible only by canoe, kayak or bigger boat.