Quite a few places around Florida will afford you a look at Red-headed Woodpeckers, but the Chinsegut Conservation Center in Brooksville stands out as one of the top spots.
The Red-headed Woodpecker is a fairly common species as far as woodpeckers go. Its range extends far beyond Florida's borders, and they can be seen all through the eastern United States and into Canada. They prefer nests in dead standing trees, where they create a cavity anywhere from 5 to 80 feet off the ground.
Here's a clip of Andy Wraithmell from the Great Florida Birding Trail leading a group at Chinsegut. FYI, the 2013 Chinsegut Birding and Wildlife Festival is being planned right now, so look for some finalized information on this event soon.
For more information on the Red-headed Woodpecker and where you can get a look at one around the state, check out the trip planning section of www.floridabirdingtrail.com. Great stuff!