You don't need visa.
US citizens don't need to apply for visa to enter Jordan, Israel and Egypt. These countries are free to enter, or you pay visa-fee at the airport after your arrival to their country.
My American client visited Jordan and Israel in June 2011.
He didn't need anything in Israel, hasn't paid any additional fees.
And he had to pay $7.50 departure tax in Jordan.
In Egypt it must be 20$.