South of Naples lies Everglades City, the western gateway to Everglades National Park. This is a water-based area, so you won't find any trails to hike or roads to drive. What you will find are boat trips out through the mangrove wilderness of the Ten Thousand Islands. This network of channels is easy to get lost in, or to lose others in. Historically, it has been a great place for rumrunners, gunrunners, alien smugglers and drug runners to hide out and/or lose their pursuers.
Start your visit at the visitor center on the second floor. Exhibits here tell the story of the mangrove ecosystem, and a little about the history of the area (like the fact that it was here in 1941 that Harry Truman dedicated Everglades National Park as the first park committed to the preservation of a wildlife habitat and not just for stunning scenery).
Next, take a boat tour out through the 10,000 islands and watch for a great variety of birdlife including ospreys and bald eagles. Manatees are frequently sighted, and Atlantic bottlenose dolphins really seem to enjoy riding along the boat's bow wake, to the delight of everyone aboard.
If you are feeling really adventurous, Everglades City is also the place to begin the 7-10 day canoe paddle along the Wilderness Waterway that connects to Flamingo at the park's extreme southern end. During the winter months, one can rent a canoe at one end of the trail, and arrange to be picked up and returned to your car when you reach the other end. Be sure to book this trip well in advance, as the backcountry campsite permits go quickly.