I am from Florida, went to UF for undergrad and it was one of the markets that I targeted for my 2L SA search.
I think if you want to work in Florida, St. Thomas would be your best bet. Since St. Thomas is in Miami, you'll have more exposure to firms and alumni practicing in S.Fl. However, it will be difficult to place anywhere outside of S.Fl. Since Coastal is in Jacksonville and the legal market there is very small, youll get less in regards to alumni and firms.
However, if you want to work outside of Florida, your choice is a bit more difficult. Cooley is more "well known" than Coastal or St. Thomas. However, it is well known for not the right reasons. It is basically (and I am not trying to sound like a male private part, more like a realist) the joke of law schools. This is because of their ridiculous and misleading rankings that they generate that puts them in the top 20 of law schools and that they are essentially a law degree mill.
Also, BigLaw will be difficult from any of these schools. However, BigLaw in Miami is your most realistic option, which requires you to attend St. Thomas and be in the top of the class.
Hope that helps!