Crar, welcome to this facination and addiction. Do a google search, there are site that you can use to find out what kind of wood grows in your area, and areas you could drive to as well.
http://forestry.about.com/library/treekey/bltree_key_id_start.htm is one that looks easy to use, you just need some of the leaves from a certain tree and it will guide you along.
http://www.sfrc.ufl.edu/extension/florida_forestry_information/forest_resources/trees_of_florida_common_hardwoods.html is a page taht shows common hardwoods in Florida. You have tons of options, ash, hornbearm,
6 types of hickory, eastern red cedar, eastern hophornbeam,
guava, about 10 types of oak,
American and Florida elm....just a feast! Now you just have to figure out where they grow, and go harvesting.
Looks like you Florida boys have it good. And sometimes wood just finds you. A huge branch feel off the maple tree in my front yard, and I got a 12" diameter, 12 foot long log out of it, as well as a few big limbs and some smaller limbs too, so it doesnt have to cost and arm and a leg.
Dane