City of Miami Beach - Apart from the extensive, excellent beach and clean water, the Art Deco Historic District is full of buildings from the 1920's-30's, most of which are hotels and public buildings, with no shortage of wacky outdoor bars scattered among them for a relaxed visual appreciation.

Drive Downtown Miami in your Exotic Car Rental- well executed high rise meets Mediterranean style, with well designed pedestrian precincts hosting excellent shops, restaurants and three museums.

Coral Gables - a classy Mediterranean style shopping and dining area; try the Biltmore Hotel for Al Capone stories; the impressive Fairchild Tropical Gardens; the Parrot Jungle; the beautiful Venetian Pool for water features.
Little Havana and Little Haiti - the two major immigrant districts are culturally interesting, with authentic restaurants and shopping, but avoid at night except for taxi travel to and from restaurants.

Short Exotic Car Rental Miami Trips:
The Everglades National Park - vast wild, wetlands area 2hrs from the city, with air boating, canoeing and lots of alligator action.

Florida Keys - mostly a few hours drive from Miami, great for diving to see the marine wildlife, sailing and beautiful exotic car driving.

Key Biscayne is the exception. It's nearby, posh, has a couple of kid-friendly museums [see Arts & Culture] , empty beaches and a large park with walking trails. 5m/8km south of Miami.
Key West is the most visited island and is still pretty though overcrowded. The Hemingway Home & Museum is popular, beaches are OK, diving your exotic rental car is great. 160/250km miles from Miami.