Naples National, The Hideout, Calusa Pines are the best...if....and that's a big if.....you can get on.
Unless you know someone, you probably can't, but, it's worth a try.
If you can't get on, try Twin Eagles (Nicklaus course....semi-private), Bonita Bay East (either course...private), Windstar(private), Hammock Bay(semi- Private, I think), Valencia (public), Palmira (private, but probably accessible), Heritage Bay (public?)
There's lots of good golf here and now is a good time to see if you can get out as most of our winter players have gone home.
Steve
Naples