Watch out!
Hour building in the States can be done without visa. The newly chances () only requires you to register for the visa waiver program BEFORE you fly, and during a transition period you will probably still have to fill out the forms in flight anyway.
But you also need a FAA PPL. That is either one you qualified for during training in the US (and kept current) OR a ‘piggy back’ FAA license which is based on your JAR PPL, and is valid as long as your JAR license and medical is valid. It is an up to three – four month process, and you can find the details in one of the sticky posts in the private flying forum, I think. You start by applying in writing to the FAA, and finish by visiting one of the local FAA offices. If you do not have this in place before you go, then forget about any flying.
Then where you rent the plane, the will give you around one hour instruction about US airspace etc. and then one-two hours check-out where you demonstrate that it is likely that you will bring the plane back in one piece. So you will demonstrate slow flight, slow speed stalls, high speed stalls, steep turns and some landings. Where I did it (
Bay Air in St. Petersburg), it was all done in a very relaxed atmosphere, with a very friendly instructor.
But remember: No FAA (Piggy back) license – No flying.