Hi Birdlady,
If all you are going to be doing is hour building, do you want the school to be JAA approved? You'll be severly limiting yourself in the choice of school.
There is *no* requirement for you to do any of your hour building at an approved JAA school, indeed some people buy their own plane to hour build.
Just because an instructor has a JAA Flight Instructor rating doesn't make him or her better than an FAA CFI. Indeed there are good and bad from both licence systems.
Indeed my FAA CPL/IR instrcutor was, in my opinion, excellent and a lot better than some instructors over on JAA land (UK).
Also the instructor will only be doing a quick checkout and maybe an FAA BFR (Bi-annual Flight Review to make you legal) anyway, that'll only take a couple of hours maximum.
Anyway if you do want a JAA approved school to rent an aeroplane from then I'd recommend Naples Air Center in Florida. They aren't the cheapest nor the most expensive but a good school, good instructors, not bad aeroplanes (their Arrow has a Garmin 430 and they also have a 1999 Cessna 172 etc).
If you want cheap then Air Desert Pacific in L.A., California. Rented there in 2000 and 2001, both on their Archers and an Arrow III. Very good prices and the instructors/staff are all pleasant and friendly. Nothing bad to say about them at all. They aren't JAA approved though.
Best wishes,
Charlie Zulu.