I have no problem recommending visitng Jordan, I was just there recently and there was no problem. The Arabs just want to sell you something.
I even saw the mountain where Aaron is buried.
Alot of Gedolim have been in Jordan this year because of Smittah, they hold that Jordan is a Safek and will buy produce from Jordan.
And lastly it wasnt Jordan that gave me a problem crossing the border, it was Israel. The Israeli kept asking me about an Israeli Passport (I dont have one and never did and I was born in NYC so I didnt understand the question)
and BTW I have been to Egypt too and had no problems there either