YOU NEED ALL YOUR CERTIFICATES AND MEDICAL CURRENT, AFTER all you need is to find any flight club who will hire you an aircraft, for private operation you can fly any aircraft it does not need to be us registered, the faa license is icao and so is recognized in all icao countries, it is only up to the aircraft owner if he wants you to fly his aircraft or not, when you go abroad you can hire cars no matter where as long as they accept your driver license, same goes for hiring aircraft for private flying.