Head for the Everglades and take an airboat ride. Depending upon the operator you select, you could learn about the Seminole tribe culture and the Everglades, all in one trip!
Take a St. John's River cruise. Again, depending upon where you do this, you can also rent a canoe or kayak for your own tour of a portion of the river.
Head for a southwest Florida beach area. Tampa Bay/St. Petersburgh is the closest to WDW, but if you head further south there are some very wonderful places, Sanibel, Captiva, Marco Island, etc. Fort De Soto, near St. Petersburgh is a very nice state park. You can fish from the pier and have a picnic/barbecue if you wanted.
St. Augustine offers tours of the surrounding bodies of water via boat, or of the town itself, via a trolley. It is a very nice place for a walking tour, as well.
Hmmm...a little tricky trying to separate activities between what is available in the US vs UK! There is a pretty good touring guide out, Florida on a Tank Full, that has a wealth of ideas for day trips.
Have fun!
