Under two months ago, I did an FAA PPL/IR at Naples Air Center - which is just down the road from Fort Myers - and was delighted with them.
Excellent instructors, aircraft in pretty good nick, prices reasonable, and an excellent airfield to fly from.
There aren't many places nearer the Everglades, if you want to go alligator spotting!
NAC were then (and I'd bet still are) OK for JAA. Whether the CAA realise that or not, I don't know, but they were certainly teaching an awful lot of Europeans for JAA licences in February/March. Sometimes there was more Dutch being spoken in the pilots' room than there was English.