Around 1980, USA had a zone (I think it was 75 miles from the border) where Mexicans were allowed to come without a green card. Is there anything like that in Egypt, Israel, Jordan, and/or Saudi Arabia? I’m interested in visiting the area shown below, but it would be inconvenient to get four multi-entry visas. I'm US citizen, rather than of any of those countries.
(I’m aware that immigration and travel rules can change at any time.)