The link that Carlos gave you or this one; http://www.miamidade.gov/transit/bus.asp ~ May help you get the public transit info. The previous link that I posted may help you find an apartment. The Airport Area in Miami, is pretty much like the Airport Area close to any major city's International Airport.
There are many aviation related businesses nearby, hotels, etc. Naturally there are many residential communities as well. Here is what comes up on the database that REALTORS use; http://sef.mlxchange.com/Pub/EmailView.asp?r=300228325&s
Also, there may be several rental communities in the area that are not included in this list.
Good Luck! Miami is a Great City!
You will want to look in http://www.miamidade.gov and look for transportation. You will find all the information about transportation. You can also look for neighborhood crime reports in that website under property information.