We started in Jordan. Flew into Amman, toured the city and spen a day in Petra.

From Petra, we traveled by bus--- and guards___ into Israel. This is the way it was done. We crossed into Israel over the Allenby Bridge. It was an unexpected emotional crossing that I will not forget. Spent several days in Israel. The memory of Yad Vashem will remain with me as long as I live!!

After Isael, we reurned the same way into Jordan to return to the US. You can ask that our passport not be stamped. Sometime it works and sometimes it does not.

What are you looking for? R&R or sightseeing? On the Israeli side you have Ein Gedi with several nice hikes, and MASSADA that is one of the most interesting archeological and historical sites in the world.

Petra - you can visit Perta from Eilat, either on your own or with a tour company. There are companies that make it as a 1 day tour too.

Not from my experience but from what others have reported the hotels on the Jordanian side are better.

I want sightseeing more & it may be easier for travellers since there be no Ramadan in Isreal.

For sightseeing there are not many sites like the Israeli Dead Sea. The drive to Eilat is also spectacular.

There will be Ramadan in Israel, but it will be felt only in Muslim populated areas, like the Old City in Jerusalem, Acre and so on. During the month of Ramadan, as far as I know,the entrance to the Temple Mount is severely restricted if not altogether prohibited for non-Muslims.