I traveled to Gainesville, FL in early September 2010. The weather was perfect! An excellent time to visit. It was still warm enough to hang out by the pool, but not so hot and humid that was uncomfortable to be outside.
The Botanical Gardens in Gainesville and amazing! Being from Colorado, I got to see a lot of vegetation and fauna that is unfamiliar to me. Also, I highly recommend the Butterfly Exhibit at the Unviersity. Especially with kids -- they loved it!