Cigar City is, in my opinion, one of the best breweries in the country, rivaling what some of the experimental west coast breweries are doing. If you can, stop by their tap room - it's centrally located (and close to the Mons, if you are into that kind of thing).
Swamp Head in Gainesville has actually been beating Cigar City for some awards, but they still have a fairly small operation with a limited lineup, and their quality still varies from batch to batch. Often, Cigar City will have some Swamp Head on tap at their location. The Swamp Heat taproom in GNV has limited hours (4-7 Wednesday through Friday), but it's right off I-75.
Besides these two, most Florida breweries are fairly forgettable or very small-scale, catering to a very regional audience.