Big Dog 2.
I suggest that you look at the thread in the wannabes forum regarding visas. believe that you will find that you can fly the C172 for fun on a visa waiver, but you most certainly cant do anything that results in a qualification, especially a jet rating for an aircraft above 12,500 lbs.
I will also second TD's comments about HPA and Mark Sterns, IMHO they run the best flight school that i have ever visited in the USA.
Enjoy the holiday.
Mutt