Since I'm the TA lurker in my family, I'm asking this on behalf of my daughter, who is about to start a 10 month stay in the Miami area working with City Year.
Her stay there begins with a few weeks of training in the downtown area before she is assigned to a school. By mid August she will have a car, but for the first week or so she will have to rely on public transit.
A lot of hostels and less expensive places to stay are near the beach areas, but I don't know how convenient it would be for her to stay there when she has to be in the downtown area during the weekdays. Eventually she will settle into a more permanent place to stay, but do you have any suggestions for places to look for her to stay for a week or two? She will need good access from the Miami airport, too.