If you're looking for public access courses, I think the best ones are closer to Marco Island. The Marriott owns 2 courses called The Rookery and Hammock Bay. Sort of semiprivate but I believe they allow public access. IMO Hammock Bay is better than most private clubs I've played in the Naples-area.
TPC Treviso Bay is open to the public after getting destroyed as a private club by the housing bust. It was in awesome shape when I played it.
I've played Calusa Pines and the Golf Club of the Everglades, which are next door to one another. GCE is a golf-only walkable track, but I know Rees Jones isn't a favorite here.
Haven't played The Hideout but now I'm intrigued, would love to play it. There is another one called Hole in the Wall that I think is kind of an old money Naples course. Dick Wilson.