There is a bus ($2.35) that goes MIA to South Beach
$2.35 AIRPORT FLYER bus service to South Beach
http://www.tripadvisor.com/ShowTopic...i_Florida.html
I just returned from 2-days in Miami, with rental car ($8/day, cheap), so you can do that too if you'd like
MIA is only 10-15 minutes away from Downtown/South Beach, in good traffic