Collier Seminole State Park sounds like what you want. Not sure where "traveling through" Naples would take you but assuming you're coming from TX, the options wouldn't be many - you'd either be heading another 10 mile south to Marco Island or you'd be going eastbound through the glades. Collier Seminole SP beside being only 20+/- miles from your Corkscrew Sanctuary is also located at the intersection of San Marco Rd which heads to Marco and Tamiami Trail (US41) which cuts through Big Cypress Swamp National Preserve and Everglades NP and is a, IMO, much better drive than Southbound (east) I75 (Alligator Alley - where you won't see any wildlife much less gators). JMO.