Cherry Pockets Fish Camp & Restaurant in Lake Wales, Florida.
http://www.cherrypocket.com/our_history
The side menu has a place to click on "Motel & RV Park"
It is a bit off the beaten path, but totally worth the drive. Frank would love the fishin'. The restaurant is in the "Florida Cracker" tradition. It's an experience! It would probably take 45-60 minutes to get to the Fort. Most of that is the trip off the main highway to get back to Cherry Pockets. We go there 2 or 3 times a year for lunch.
Good for 2-3 days....or in Frank's case...2-3 weeks.
Not sure if you'd use the GC much, though. You can, just don't know that you would.
Another place is River Ranch - also in Lake Wales. It's not cheap, though.
Lots of fun, good fishin', not cheap.
http://www.wgriverranch.com/
ETA: The State Parks in the area are total crap. I don't recommend them at all, Denise. Donnie might chime in with some info about Turkey Lake near Universal. He stays there a lot when he can't get into the Fort or doesn't want to spring full price for the Fort. He says it's really nice.
Also - a little further away is Jetty Park at Cape Canaveral. You would not use the GC at all, but you'd see the cruise ships come and go, and you can fish in the Atlantic off a beautiful pier. You might want to check that out.