It's illegal to take anything older than 50 years old out of navigable Florida waters and it's a big fine.
That being said, all the rivers have points in them but the best hunting is in the clear rivers. Any spring feed river will do. Alligators and water moccassins will be there but you probably won't see them. Alligators often leave at the sound of an outboard motor. I don't worry about gators that are less than 6 feet long. Other opinions may vary.
Look for a hard bottom on the river you are searching. Sandy bottoms make it too hard to find heavy objects. Rock beds are primo.
You'll get in less trouble looking for fossils which are found using the exact same techniques. When we hunt for fossils, we go to a clear river, usually in 8 feet or less water, get over weighted to help fight the current, and lay on the bottom, slowly searching the area. If you don't see a lot of small rocks in the area you are hunting you may be wasting your time.