hi seagull61,
i am sure others with have up to date info for you...but pre JAA i got that done.
all countries that are signatories to the ICAO convention must accept the basic ppl licence...(not the ratings on it though) of another state who is also a singatory..
i think you will find that if you take that into your nearest FAA office they will give you a basic PPL..(airmans certificate i think they call it ), which will be valid as long as and subject to any conditions applying to your JAA licence. as i said you can only use it PPL VFR even if it has an instrument rating on it you will not be entitled to use that in us airspace..
now how 9/11 may have changed the system i cannot say because i think unlike the old pice of paper they handed out you now probably have to go through security ( to train in the usa anyway) and i think the licence now has security details electronically printed on it...but as i say i am sure some guys with a more intimate knowledge of to-days requirements will help you..
good luck...
the dean.