I had been planning to visit this year for my first time The Senator which just burned down. That bald cypress was about 3,500 years old.http://www.npr.org/blogs/thetwo-way/2012/01/17/145342304/one-of-worlds-oldest-cypress-trees-the-senator-burns-in-florida
Hopefully the Florida park services department will do a better job at protecting Lady Liberty at a youthful 2,000 years old.
Anyone in Florida interested in seeing mature baobabs can enjoy them on the lawn of the Bass Museum in Miami Beach, though sadly they've been badly scarred over the years by idiots carving initials into them.
There are a few champion trees at Flamingo Gardens, west of Fort Lauderdale, And Fairchild Tropical Gardens in south Miami has what I think is the largest depository of different types of palm trees in the country.
Florida also has Disney's tree of life which I thought was going to be totally hokey but turned out to be pretty fun.